EFFECT OF TIME ON THE TENSILE STRENGTH OF SEVERAL
BUSHVELD COMPLEX ROCK TYPES
David Nyungu
A Dissertation submitted to the Faculty of Engineering and the Built Environment,
University of the Witwatersrand, in fulfilment of the requirements of the degree of
Master of Science in Engineering.
Johannesburg 2013
Effect of time on the tensile strength of several Bushveld Complex rock types
ii
DECLARATION
I declare that this dissertation is my own unaided work. It is being submitted for the
degree of Master of Science in Engineering to the University of Witwatersrand,
Johannesburg. It has not been submitted before for any degree or examination to
any other University.
................................................................................................................................
(Signature of Candidate)
...................day of............................year.......................................
day month year
Effect of time on the tensile strength of several Bushveld Complex rock types
iii
DEDICATION
“A Rock Engineer falls at least once in his life because he is expected to look up
more than down”, (Anonymous). I am gratified to have family and acquaintances in
my life to pick me up whenever I fall.
ACKNOWLEDGEMENTS
Mr Henry Chiwaye, for his assistance with the numerical models used in this
research.
Effect of time on the tensile strength of several Bushveld Complex rock types
iv
Abstract
Despite observations of spalling and damage of Bushveld Complex (BC) mine
excavation wall rock over the passage of time, there have been very few time-
dependent or creep tests carried out in South Africa on rock, particularly on BC rock
types. The research detailed in this dissertation deals with the investigation of stress
and strain conditions influencing spalling of wall rock in BC mine excavations, and
the influence of time on the tensile strength of several BC rock types. The research
includes a review of the BC mining environment; a review of literature relevant to
time-dependent behaviour of rock; laboratory testing of BC rocks in uniaxial
compression and in indirect tension; time-dependent laboratory testing in indirect
tension; and elastic numerical modelling of typical BC mine excavations. The results
show that the magnitude of the tensile strength of BC rock types is approximately 5%
of their uniaxial compressive strength magnitudes. The long term uniaxial
compressive strength of the BC rocks, interpreted from the axial stress-volumetric
strain graphs in the UCS test is on average 78MPa, which is 56% of the UCS value.
The tensile strength of the BC rock types was found to be time-dependent. However,
ultimate minimum long term tensile strength values could not be determined in this
research owing to limited testing machine availability. Although the individual test
specimen failure times showed large variations, logarithmic time-to-failure trends of
the nine test categories in the research showed a general time-dependent behaviour.
The long term tensile strength is shown to be less than 70% of the normal tensile
strength. Extension strains at tensile strength failure ranged between 1.6 x 10-4 and
2.1 x 10-4. Values corresponding with the long term tensile strength are less than
70% of this range, namely, less than 1.1 x 10-4 to 1.5 x 10-4. The time-dependent
data presented in the dissertation represent new knowledge, since such rock testing
and analysis does not appear to have been carried out before on BC rock types.
The compressive stresses determined in the numerical models were found to be an
order of magnitude lower than the compressive strength of the rock. Tensile
stresses in the models were of comparable magnitude to the tensile strength of the
BC rock types investigated in this research. The numerical models showed that
large zones of extension strain can occur around BC excavations, and that the
magnitudes of the extension strain can substantially exceed the critical values
Effect of time on the tensile strength of several Bushveld Complex rock types
v
determined from the laboratory testing. There is no conclusive prerequisite for tensile
conditions to exist, to induce critical extension strain. The implication of this is that
there are substantial zones surrounding BC mine excavations that will be prone to
spalling conditions and perhaps more significant failure.
Effect of time on the tensile strength of several Bushveld Complex rock types
vi
Table of contents
DECLARATION ........................................................................................................... ii
DEDICATION ............................................................................................................. iii
ACKNOWLEDGEMENTS .......................................................................................... iii
Abstract ...................................................................................................................... iv
List of Figures ............................................................................................................. ix
List of Tables ............................................................................................................ xvi
List of Symbols ........................................................................................................ xvii
CHAPTER 1 ............................................................................................................... 1
INTRODUCTION ........................................................................................................ 1
1.1 Background ....................................................................................................... 1
1.2 Definition of the problem ................................................................................... 3
1.3 Research objectives .......................................................................................... 5
1.4 Research methodology ..................................................................................... 6
1.5 Content of the dissertation ................................................................................ 7
CHAPTER 2 ............................................................................................................... 8
CHARACTERISTICS AND ANALYSIS OF THE BUSHVELD COMPLEX MINING
ENVIRONMENT ......................................................................................................... 8
2.1 Introduction ....................................................................................................... 8
2.1.1 Geology of the Bushveld Complex .............................................................. 8
2.1.2 Stratigraphy of the Bushveld Complex ...................................................... 10
2.1.3 The Bushveld Complex rock types ........................................................... 13
2.2 Behaviour of rock under stress ....................................................................... 15
2.2.1 In-situ stress conditions of the Bushveld Complex .................................... 15
2.2.2 Behaviour of intact rock under stress ........................................................ 17
2.2.3 Characteristics of rock failure .................................................................... 26
2.3 Time-dependent characteristics of rock .......................................................... 28
Effect of time on the tensile strength of several Bushveld Complex rock types
vii
2.3.1 Time-dependent behaviour in rock ........................................................... 28
2.4 Summary and conclusions .............................................................................. 34
CHAPTER 3 ............................................................................................................. 36
STRESS AND STRAIN ANALYSIS .......................................................................... 36
3.1 Introduction ..................................................................................................... 36
3.1.1 Mining methods used in the Bushveld Complex ....................................... 36
3.2 Characteristic geometries of Bushveld Complex mine excavations ................ 39
3.2.1 Geometries of an in-stope pillar ................................................................ 39
3.2.2 Geometries of a mining stope ................................................................... 40
3.2.3 Geometries of an incline shaft .................................................................. 41
3.3 Numerical and analytical methods .................................................................. 41
3.3.1 Review of numerical methods in mining ................................................... 42
3.3.2 Stress-strain analysis objectives ............................................................... 43
3.3.3 Methodology for stress and extension strain analysis ............................... 44
3.4 Stress and extension strain analysis ............................................................... 44
3.4.1 Analysis of results - in-stope pillar model .................................................. 45
3.5 Conclusion ...................................................................................................... 56
CHAPTER 4 ............................................................................................................. 57
LABORATORY TESTS ON BUSHVELD COMPLEX ROCKS ................................. 57
4.1 Introduction ..................................................................................................... 57
4.1.1 Testing objectives ..................................................................................... 57
4.1.2 Testing methodology ................................................................................ 58
4.1.3 Spatial location of core samples ............................................................... 58
4.1.4 Distribution of test specimens ................................................................... 59
4.1.5 Preparation of test specimens .................................................................. 61
4.2 The UCS test set up ........................................................................................ 62
4.3 Analysis of UCS test results ............................................................................ 63
Effect of time on the tensile strength of several Bushveld Complex rock types
viii
4.3.1 Processing of UCS test results ................................................................. 63
4.3.2 Deformation properties ............................................................................. 65
4.3.3 Analysis of volumetric strain ..................................................................... 66
4.3.4 UCS test results summary ........................................................................ 67
4.4 Brazilian Indirect Tensile (BIT) strength test ................................................... 68
4.4.1 Normal Brazilian Indirect Tensile (BIT) strength test ................................. 69
4.4.2 Time-dependent Brazilian Indirect Tensile (BIT) strength test .................. 72
4.4.3 Time-dependent BIT test results ............................................................... 75
4.5 Conclusions .................................................................................................... 78
CHAPTER 5 ............................................................................................................. 80
DISCUSSION OF STRESS-STRAIN ANALYSIS RESULTS ................................... 80
5.1 Introduction ..................................................................................................... 80
5.2 Results of laboratory testing ............................................................................ 80
5.3 Results of the numerical analyses .................................................................. 81
5.3 Implications from the numerical analyses and the laboratory testing .............. 84
CHAPTER 6 ............................................................................................................. 85
CONCLUSIONS AND RECOMMENDATIONS ........................................................ 85
REFERENCES ......................................................................................................... 88
APPENDICES .......................................................................................................... 99
Appendix A: Geological log sheet for drill hole BH6082 ........................................ 99
Appendix B: Laboratory rock strength test results ............................................... 107
B1 UCS test results and long term strength analysis ....................................... 107
B2 Normal Brazilian Indirect Tensile (BIT) strength test results ....................... 117
B3 Time-dependent Brazilian Indirect Tensile (BIT) Strength test results ........ 118
Appendix C: Numerical modelling results (Stress and strain analysis) ............... 126
C1 Stress and strain analysis: Incline shaft ..................................................... 126
C2 Stress and strain analysis: mining stope .................................................... 132
Effect of time on the tensile strength of several Bushveld Complex rock types
ix
List of Figures
Figure 1-1: Spalling in a haulage observed in a platinum mine located in
the western limb of the Bushveld Complex .............................................. 2
Figure 1-2: Advance Strike Gully (ASG) stress induced fractures in a deep
gold mine ................................................................................................. 3
Figure 1-3: Spalling in a strike orientated pillar in a platinum mine ............................ 4
Figure 1-4: Excavation wall damage and fracture extension observed in
BC mines ................................................................................................. 4
Figure 2-1: Geology map of the Bushveld Complex (after Viljoen and
Schürmann, 1998) ................................................................................... 9
Figure 2–2: Typical stratigraphy of the Bushveld Complex ...................................... 10
Figure 2-3: Lithographic representation of the Bushveld Complex
(Rangasamy, 2010) ............................................................................... 11
Figure 2-4: Schematic cross-section of the upper portion of the Upper
Critical Zone of the Rustenburg Layered Suite, at Northam
Platinum Mine (Smith and Basson, 2006) .............................................. 13
Figure 2-5: Ratio of the principal horizontal stress to the principal vertical
stress for South African mines, (after Stacey and Wesseloo,
2004). .................................................................................................... 16
Figure 2-6: Stress induced failure in the roof of a dip oriented tunnel in a
platinum mine, (Stacey and Wesseloo, 2004) ....................................... 17
Figure 2-7: Failure modes in compression (Ashby and Hallam, 1986) ..................... 18
Figure 2-8: Crack branching mode under compressive loading (Halm and
Dragon, 1998) ........................................................................................ 20
Figure 2-9: Mechanism of brittle fracture under multi-axial compression,
Bieniawski, (1967) ................................................................................. 21
Figure 2-10: Tensile strength testing set up, a) The dog bone shaped
specimen used in direct tensile strength tests (Ryder and
Effect of time on the tensile strength of several Bushveld Complex rock types
x
Jager, 2002) and b) Brazilian disc set up used in indirect
tensile strength tests .............................................................................. 24
Figure 2-11: Creep curve showing different stages of deformation of rocks
(Dubey and Gairola, 2008) .................................................................... 30
Figure 2-12: Principle of operation of the CSIR creep testing machine
(Drescher and Handley, 2003) ............................................................... 30
Figure 2-13: Extension fracturing in an unsupported clay tunnel (Blumling
et al, 2007) ............................................................................................. 33
Figure 2-14: Time-dependent stope creep closure (Malan et al, 2007) .................... 34
Figure 2-15: Continuous stope closure after blasting and the definition of
closure terms, (Malan et al, 2007) ......................................................... 34
Figure 3-1: Conventional breast mining layout in the UG2 reef. After
(Egerton, 2004) ...................................................................................... 37
Figure 3-2: A typical room and pillar mining layout. After (Egerton, 2004) ............... 38
Figure 3-4: Modelling geometries of a 29 m by 1.8 m high stope ............................. 40
Figure 3-5: Modelling geometry of a 7 m wide by 4 m high incline shaft .................. 41
Figure 3-6: Extension of damaged zone for different time progressions in
a section located 6 m behind the tunnel face (Bonini et al,
2009) ..................................................................................................... 42
Figure 3-7: Distribution of Major Principal Stress (σ1) at a depth of 500m
with a k-ratio = 1 .................................................................................... 45
Figure 3-8: Distribution of Major Principal Stress (σ1) at a depth of 500m
with a k-ratio = 2 .................................................................................... 46
Figure 3-9: Distribution of Major Principal Stress (σ1) at a depth of 1000m
with a k-ratio = 1 .................................................................................... 46
Figure 3-10: Distribution of Major Principal Stress (σ1) at a depth of
1000m with a k-ratio = 2 ........................................................................ 47
Figure 3-11: Distribution of Minor Principal Stress (σ3) at a depth of 500m
with a k-ratio = 1 .................................................................................... 48
Effect of time on the tensile strength of several Bushveld Complex rock types
xi
Figure 3-12: Distribution of Minor Principal Stress (σ3) at a depth of 500m
with a k-ratio = 2 .................................................................................... 48
Figure 3-13: Distribution of Minor Principal Stress (σ3) at a depth of
1000m with a k-ratio = 1 ........................................................................ 49
Figure 3-14: Distribution of Minor Principal Stress (σ3) at a depth of
1000m with a k-ratio = 2 ........................................................................ 49
Figure 3-15: Distribution of extension strain at a depth of 500m with a k-
ratio = 1.................................................................................................. 51
Figure 3-16: Distribution of extension strain at a depth of 500m with a k-
ratio = 2.................................................................................................. 51
Figure 3-17: Distribution of extension strain at a depth of 1000m with a k-
ratio = 1.................................................................................................. 52
Figure 3-18: Distribution of extension strain at a depth of 1000m with a k-
ratio = 2.................................................................................................. 52
Figure 3-19: Distribution of Critical Extension strain at a depth of 500 m
and k = 2 ................................................................................................ 53
Figure 3-20: De-lamination of hanging wall strata .................................................... 54
Figure 3-21: Hanging wall damage under tensile stresses in a stope ...................... 55
Figure 3-22: Spalling parallel to the haulage walls induced by extension
strain observed in a FW haulage mined in anorthositic norite ............... 55
Figure 4-1: Graphical presentation of the distribution of test specimen .................... 61
Figure 4-2: Rock specimens for UCS and BIT test shapes ...................................... 62
Figure 4-3: The Amsler testing machine ................................................................... 62
Figure 4-5: Stress-Strain graph for mottled anorthosite specimen UCA7 ................. 65
Figure 4-6: Failure mode observed in specimen tested in uniaxial
compression, (a) before the test and (b) after the test ........................... 65
Figure 4-7: Determination of the “long term strength” for specimen (UCA7) ............ 66
Figure 4-8: The MTS 815 rock testing machine used to load BIT discs ................... 68
Effect of time on the tensile strength of several Bushveld Complex rock types
xii
Figure 4-9: Curved platens used in the BIT test set up, (a) before the test
and (b) after the test .............................................................................. 68
Figure 4-10: Normal BIT load-time plot .................................................................... 69
Figure 4-11: Specimen failure in the BIT test ........................................................... 71
Figure 4-12: Calculated strains at various load levels for the nine test
categories .............................................................................................. 73
Figure 4-13: Time-dependent Load-Time plot .......................................................... 74
Figure 4-14: Time-dependent BIT Load-Time plot ................................................... 74
Figure 4-15: Time-to-failure plot for test category B (Rock type: spotted
anorthositic norite) ................................................................................. 76
Figure 4-16: Load-Time plot for averages of all the test results ............................... 77
Figure 4-17: Percentage load-Time plot for averages of all test results ................... 77
Figure 4-18: Strain-Time plot for averages of all test results .................................... 78
Figure 5-1: Distribution of extension strain around an in-stope pillar ........................ 82
Figure 5-2: Illustration of the zone in a stope sidewall prone to fracture
propagation ............................................................................................ 83
Figure 5-3: Illustration of zones in the stope hanging wall prone to fracture
propagation ............................................................................................ 83
Figure B1-1: Stress-strain graph for spotted anorthositic norite (S.A.N.)
rock type specimen UCB6 ................................................................... 108
Figure B1-2: Stress-strain graph for pyroxenite (P.) rock type specimen
UCC8 ................................................................................................... 108
Figure B1-3: Stress-strain graph for mottled anorthosite (M.A.) rock type
specimen UCD10................................................................................. 109
Figure B1-4: Stress-strain graph for norite (N.) rock type specimen UCE7 ............ 109
Figure B1-5: Stress-strain graph for spotted anorthositic norite (S.A.N.)
rock type specimen UCF6 ................................................................... 110
Effect of time on the tensile strength of several Bushveld Complex rock types
xiii
Figure B1-6: Stress-strain graph for anorthositic norite (A.N.) rock type
specimen UCG7 .................................................................................. 110
Figure B1-7: Stress-strain graph for spotted anorthosite (S.A.) rock type
specimen UCH7................................................................................... 111
Figure B1-8: Stress-strain graph for mottled anorthosite (M.A.) rock type
specimen UCI9 .................................................................................... 111
Figure B1-9: Rate of change of volumetric strain with respect to stress
(UCB6) ................................................................................................. 112
Figure B1-10: Rate of change of volumetric strain with respect to stress
(UCC8) ................................................................................................ 113
Figure B1-11: Rate of change of volumetric strain with respect to stress
(UCD10) .............................................................................................. 113
Figure B1-12: Rate of change of volumetric strain with respect to stress
(UCE7) ................................................................................................. 114
Figure B1-13: Rate of change of volumetric strain with respect to stress
(UCF6) ................................................................................................. 114
Figure B1-14: Rate of change of volumetric strain with respect to stress
(UCG7) ................................................................................................ 115
Figure B1-15: Rate of change of volumetric strain with respect to stress
(UCH10) .............................................................................................. 115
B1-16: Rate of change of volumetric strain with respect to stress (UCI9) .............. 116
Figure B3-1: Time-to-failure plots: (mottled anorthosite) ........................................ 121
Figure B3-2: Time-to-failure plots: (spotted anorthositic norite) .............................. 122
Figure B3-3: Time-to-failure plots: (pyroxenite) ...................................................... 122
Figure B3-4: Time-to-failure plots: (mottled anorthosite) ........................................ 123
Figure B3-5: Time-to-failure plots: (norite) .............................................................. 123
Figure B3-6: Time-to-failure plots: (spotted anorthositic norite) .............................. 124
Figure B3-7: Time-to-failure plots: (anorthositic norite) .......................................... 124
Effect of time on the tensile strength of several Bushveld Complex rock types
xiv
Figure B3-8: Time-to-failure plots: (spotted anorthosite) ........................................ 125
Figure B3-9: Time-to-failure plots: (mottled anorthosite) ........................................ 125
Figure C1-1: Major Principal Stress at a depth of 500m with k-ratio = 1 ................ 126
Figure C1-2: Major Principal Stress at a depth of 500m with k-ratio = 2 ................ 127
Figure C1-3: Major Principal Stress at a depth of 1000m with k-ratio = 1 .............. 127
Figure C1-4: Major Principal Stress at a depth of 1000m with k-ratio = 2 .............. 128
Figure C1-5: Minor Principal Stress at a depth of 500m with k-ratio = 1 ................ 128
Figure C1-6: Minor Principal Stress at a depth of 500m with k-ratio = 2.
The depth of influence of low compressive and tensile
stresses is indicated ............................................................................ 129
Figure C1-7: Minor Principal Stress at a depth of 1000m with k-ratio = 1 .............. 129
Figure C1-8: Minor Principal Stress at a depth of 1000m with k-ratio = 2 .............. 130
Figure C1-9: Extension strain at a depth of 500m with k-ratio = 1 .......................... 130
Figure C1-10: Extension strain at a depth of 500m with k-ratio = 2 ........................ 131
Figure C1-11: Extension strain at a depth of 1000m with k-ratio = 1 ...................... 131
Figure C1-12: Extension strain at a depth of 1000m with k-ratio = 2 ...................... 132
Figure C2-1: Major Principal Stress at a depth of 500m with k-ratio = 1 ................ 133
Figure C2-2: Major Principal Stress at a depth of 500m with k-ratio = 2 ................ 133
Figure C2-3: Major Principal Stress at a depth of 1000m with k-ratio = 1 .............. 134
Figure C2-4: Major Principal Stress at a depth of 1000m with k-ratio = 2 .............. 134
Figure C2-5: Minor Principal Stress at a depth of 500m with k-ratio = 1 ................ 135
Figure C2-6: Minor Principal Stress at a depth of 500m with k-ratio = 2 ................ 135
Figure C2-7: Minor Principal Stress at a depth of 1000m with k-ratio = 1 .............. 136
Figure C2-8: Minor Principal Stress at a depth of 1000m with k-ratio = 2 .............. 136
Figure C2-9: Extension strain at a depth of 500m with k-ratio = 1 .......................... 137
Figure C2-10: Extension strain at a depth of 500m with k-ratio = 2 ........................ 137
Figure C2-11: Extension strain at a depth of 1000m with k-ratio = 1 ...................... 138
Effect of time on the tensile strength of several Bushveld Complex rock types
xv
Figure C2-12: Extension strain at a depth of 1000m with k-ratio = 2 ...................... 138
Effect of time on the tensile strength of several Bushveld Complex rock types
xvi
List of Tables
Table 4-1: Exploration drill hole coordinates ............................................................ 58
Table 4-2: Specimen nomenclature.......................................................................... 59
Table 4-3: Distribution of test specimens ................................................................. 60
Table 4-4: Recorded UCS test values for specimen UCA7 ...................................... 64
Table 4-5: Summaries of UCS test results (average values are presented
here) ...................................................................................................... 67
Table 4-6: Summaries of Normal Brazilian Indirect Tensile BIT strength
test results ............................................................................................. 70
Table 4-7: Comparison of UCS and BIT strength test .............................................. 70
Table 4-8: Time-dependent BIT test loads ............................................................... 72
Table 4-9: Time-dependent test results .................................................................... 75
Table B1-1: Uniaxial compressive strength test results ......................................... 107
Table B2-2: Normal Brazilian Indirect Tensile (BIT) strength test results .............. 117
Table B3-3: Time-dependent Brazilian Indirect Tensile (BIT) strength test
results .................................................................................................. 118
Effect of time on the tensile strength of several Bushveld Complex rock types
xvii
List of Symbols
2-D 2-Dimensional numerical modelling
AE Acoustic Emission
ASG Advance Strike Gully
BC Bushveld Complex
BIT Brazilian Indirect Tensile strength test
BRC Bottom Reef Contact
Cr/Fe Chrome to iron ratio
Cr2O3 Chromite
D Diameter of a rock drill core sample
FW Footwall
HW Hangingwall
ISRM International Society of Rock Mechanics
km kilometre(s)
km2 Square kilometre(s)
kPa kilo Pascal(s)
L/D length to diameter ratio of a cylindrical rock
specimen
LG Lower Group
m metre(s)
m2 Square metre(s)
Ma Megaannum
MG Middle Group
mm millimetre(s)
MPa Mega Pascal(s)
MR Merensky Reef
MTS Multiple Testing System
NBA - NBI Normal Brazilian tensile strength test samples
P Load at failure in the Brazilian Indirect Tensile
strength test
PGE Platinum Group Elements
PGMs Platinum Group Metals
Effect of time on the tensile strength of several Bushveld Complex rock types
xviii
Phase 2 An elastic 2-D numerical modelling software
r.t.p. Room temperature pressure
R Radius of the Brazilian test disc
SEM Scanning Electron Microscope
SW Sidewall
t/D thickness to diameter ratio of a Brazilian Disc
Specimen
T(s) Time in seconds
TRC Top Reef Contact
TB%A - TB%I Time-dependent Brazilian tensile strength test
samples
UG Upper Group
UG2 PGE bearing reef type called the Upper Group 2
UCA - UCI Uniaxial Compressive strength test samples
E Young’s Elastic Modulus
σ1, σ2 and σ3 Major, Intermediate and Minor Principal Stress
σt Direct or indirect tensile strength
σc Uniaxial Compressive Strength
° Angular measurement in Degrees
k k-ratio = horizontal stress/vertical stress
ε1, ε2 and ε3 Major, Intermediate and Minor Principal strain
εr, εa Radial strain and axial strain
v Poisson’s ratio
π Pi = 3.14 to two decimal places
Effect of time on the tensile strength of several Bushveld Complex rock types
1
CHAPTER 1
INTRODUCTION
1.1 Background
South Africa is a key metals mining and minerals processing power house of the
world and is host to a wide range of the world’s largest mineral resources. Precious
metal resources in South Africa occur mainly in the Witwatersrand Basin (gold,
uranium) (Namakando, 2006) and the Bushveld Complex (PGMs, chrome ore). The
nation is a major producer of gold and base metals and hosts most of the world’s
mineral reserves of Platinum Group Metals (PGMs) – 89% (about 75% and 50% of
the world’s reserves of platinum and palladium respectively (Hilliard, 1996;
Cawthorn, 1999; and Chamber of Mines, 2010). The same amount of reserves of
PGMs and gold are found at deep levels, currently being slowly exploited, but with
future production potential estimated to last more than a hundred years. Cawthorn
(1999) suggests that, since mining of PGMs in the Bushveld Complex (BC) has only
progressed to an average of 2000m below surface, the proven reserves may easily
double with increases in mining depth. Underground mines contribute the bulk of
PGMs and gold production in South Africa (Internet: Hilliard, 1997). In underground
operations, primary and secondary excavations are mined to access the mineral
reserves and these have to remain open and stable for the life of mine.
The bulk of the PGM ore is mined at depths between 500m and 2000m below
surface. At shallow depth high horizontal stress conditions prevail, due possibly to
tectonics, with horizontal to vertical stress ratios ranging between 0.8 and 4.5
(Stacey, 2002). These stress conditions can induce spalling fractures in tunnel
hanging walls (Ryder and Jager, 2002). Spalling refers to a failure process involving
extensional splitting cracks (Fairhurst and Cook, 1966). Figure 1-1 illustrates the
propensity for excavation walls to experience spalling at a depth approximately 400m
below surface observed in a Bushveld Complex platinum mine. The walls of the
Effect of time on the tensile strength of several Bushveld Complex rock types
2
haulage were observed to scale from the exposed outside wall surfaces inwards into
the rock mass with the passage of time. Without the confinement provided by
shotcrete, mesh and lacing, loss of wall rock material through fall out of slabs of wall
rock leads to loss of confinement, with subsequent exposure of fresh rock surfaces
susceptible to the same damage.
Figure 1-1: Spalling in a haulage observed in a platinum mine located in the western limb of the Bushveld Complex
In contrast, pronounced and predictable stress-induced fractures are observed in
excavation walls in deep level gold mines, (Figure 1-2) with a shorter onset time
(days to weeks) than is observed in shallow Bushveld Complex mines, where
fractures develop months to years after excavation.
Effect of time on the tensile strength of several Bushveld Complex rock types
3
.
Figure 1-2: Advance Strike Gully (ASG) stress induced fractures in a deep gold mine
In shallow BC mines (average 500 m below surface), the rock compressive strength
(UCS) is usually greater than the compressive stress in the excavation walls. In
these stress conditions surface fractures take months to years to appear and
propagate at very slow rates.
1.2 Definition of the problem
Time-dependent spalling of excavation wall rock material has been observed in the
BC mines, occurring months to years after excavation due to fracture initiation and
propagation in intact rock, (Figure 1-1) and (Figure 1-3). According to Ryder and
Jager (2002), the creep rate in rock is dependent on the magnitude of the deviatoric
stress (σ1 - σ3) and not the individual magnitudes of σ1 and σ3, where σ1 and σ3 are
the major and minor principal stresses respectively. Creep activity is therefore more
pronounced close to the exposed excavation walls (i.e. the sidewall and the hanging
wall) where the deviatoric stresses are large and confining stresses are low.
Effect of time on the tensile strength of several Bushveld Complex rock types
4
Figure 1-3: Spalling in a strike orientated pillar in a platinum mine
Damage in excavation walls in the BC mines is exacerbated by the intersection of
fractures with naturally-occurring, shallow dipping discontinuities and layered rock,
resulting in the formation of blocks of rock with high fall out and unravelling potential,
as sketched in Figure 1-4.
Figure 1-4: Excavation wall damage and fracture extension observed in BC mines
Effect of time on the tensile strength of several Bushveld Complex rock types
5
The minimum principal stress in the wall rock in BC mine excavations is low
compressive and occasionally tensile, usually lower than the respective compressive
and tensile strengths of the host rock material. However, in such conditions,
significant magnitudes of extension strain may occur. An analysis of the stress
conditions, together with an assessment of the mechanisms of excavation wall rock
damage in typical BC mine excavations, is therefore very important in the design of
life of mine excavations. Despite the importance of the current discussion, there
have been very few studies on time-dependent and tensile creep in rock (Zhao,
2011), more so on BC rock types. Extension characteristics and the effect of time on
the tensile strengths of several BC rock types are the focus of the research
presented in this dissertation.
1.3 Research objectives
This research investigates the phenomenon of stress induced fracturing in, and time-
dependent tensile strength characteristics of BC mine excavation wall rocks. The
following objectives are highlighted:
Provide a background to the characteristics of the BC mining environment and
the associated excavation wall stability problems.
Explore the distributions of stresses around BC mine excavations.
Evaluate the compressive and tensile strength and deformation
characteristics of several BC rock types, assessing the implications of these
results to mining in the Bushveld Complex.
Investigate extension strain distributions around typical BC mine excavations,
contrasting the magnitudes of the strain values calculated in numerical
analyses with the strain values at failure from laboratory tests.
Investigate the time-dependent characteristics of the tensile strength of
several BC rock types subjected to constant indirect tensile stresses lower
than their tensile strengths.
The methodology followed in conducting this research follows.
Effect of time on the tensile strength of several Bushveld Complex rock types
6
1.4 Research methodology
The methodology adopted for this research includes:
Review of the BC mining environment focusing on the following:
Relating the BC geology and characteristics of the BC rock types,
Outlining the mining methods amenable to mining the BC PGM ore
reserves, and typical excavation types used in the BC mines, and
Investigating in-situ stress characteristics in the BC Mines
Review of failure of rock under stress, focusing on:
Investigating fracture mechanisms in rock under low normal stress levels
and the associated failure mode, and
Outlining laboratory compressive, tensile and time-dependent (creep) rock
testing methods
Review the application of numerical modelling in time-dependent (rheological)
rock masses
Carry out numerical analysis of stress and strain around models of typical BC
excavations, using rock properties derived from laboratory test results, to
investigate the zones of critical extension strain (zones of potential fracture
initiation)
Conducting laboratory uniaxial compressive strength (UCS) and Brazilian
indirect tensile (BIT) strength tests to establish the intact rock strengths and
elastic properties of several BC rock types.
Conducting time-dependent BIT strength tests on several BC rock types,
establishing their time-to-failure under predetermined constant stress levels
derived as fractions of the tensile strength of the respective rock types (0.7;
0.75; 0.8; 0.85 and 0.9 x σt).
A comparison is made between strain values calculated from laboratory tests and
magnitudes of extension strain values obtained from numerical models, and the
resulting implications on the stability of the excavations are discussed. Time-to-
Effect of time on the tensile strength of several Bushveld Complex rock types
7
failure values from time-dependent tensile creep tests are recorded and analysed, to
investigate time-dependent trends in the tensile strength of several BC rock types.
1.5 Content of the dissertation
Chapter 2 gives the characteristics of the Bushveld Complex (BC) mining
environment, and a review of the laboratory test methods and the behaviour of rock
under various stress conditions. Characteristic mine excavations prescribed by the
BC mining environment, and stress-strain analysis conducted on model excavations
based on the BC mining set up, are presented in Chapter 3. Chapter 4 reports
results of laboratory tests on several BC rock types aimed at investigating their
elastic properties, long term strength and time-dependent characteristics under
indirect tension. Discussions of the findings, and comparison of stress-strain analysis
results and laboratory test results, are covered in Chapter 5. The final chapter gives
the conclusions and recommendations from the research.
Effect of time on the tensile strength of several Bushveld Complex rock types
8
CHAPTER 2
CHARACTERISTICS AND ANALYSIS OF THE BUSHVELD
COMPLEX MINING ENVIRONMENT
2.1 Introduction
The Bushveld Complex (BC) is host to the world’s most important Platinum Group
Metals (PGMs) reserves. As such it is imperative to understand the structural
properties of the PGMs ore reefs and hosting environment that prescribe the current
choice of mining methods utilised in the BC mines. This entails outlining the
characteristic BC geology, in-situ and induced stress conditions and mechanical
properties of the rock types hosting the BC mine excavations. With this aim
numerical stress analyses and laboratory rock strength tests have been carried out.
2.1.1 Geology of the Bushveld Complex
Drill core from Impala Platinum Mines’ surface exploration drilling projects in its
Rustenburg division was used in this research to investigate the strength and
deformational characteristics of several BC rock types. The spatial location in the BC
and a typical lithographic description of the test drill core used in this research are
provided here. Different hypotheses have been raised regarding the possible
formation and genesis of the Bushveld Complex mineralization by Cawthorn (1999),
Mitchell and Manthree (2002), Seabrook et al (2002), Brown (2005), Cawthorn et al
(2006), Simmat et al (2006), Smith and Basson (2006), Wilson and Chunnett (2006),
Perrit and Roberts (2007), and Naldrett et al (2009), but these are not debated in
detail here. Simplistically “the Bushveld Complex formed by the repeated injections
of lava (or magma) into a sub-volcanic, shallow-level chamber. With differential
cooling different sub-horizontal mineral accumulations were formed starting from the
base of the depositional chamber now commonly known as the Bushveld Complex
(BC). Subsequent feeding of molten magma into this chamber resulted in intervals of
repeated mineral accumulations with important concentrations of minor minerals like
chromicise and vanadium” (Cawthorn, 1999). Figure 2-1 shows a geological map of
Effect of time on the tensile strength of several Bushveld Complex rock types
9
the Bushveld Complex giving the locations of some of the operations of Impala
Platinum Mines.
Figure 2-1: Geology map of the Bushveld Complex (after Viljoen and Schürmann, 1998)
The 2060 Ma old (BC) is an irregular, saucer shaped massive layered igneous
intrusion, with outcrop extremities of ∼450 km east–west and ∼300 km north–south
(Simmat et al, 2006). “The (BC) platinum reserves consist of three different reefs; the
Merensky reef (MR), the Upper Group 2 (UG2) chromicise reef, both of these can be
traced on surface for about 300 kilometres in two separate horizons, and the Platreef
which extends for 30 kilometres” (Cawthorn, 1999; 2006). Below these reef horizons
lies the Upper Group 1 (UG1) reef, the platinum content of which has not yet been
widely proven to be economically viable. The down-dip continuity of these reefs has
been confirmed at just more than 3000m below surface for the Merensky and UG2
reefs (Cawthorn, 1999).
Effect of time on the tensile strength of several Bushveld Complex rock types
10
2.1.2 Stratigraphy of the Bushveld Complex
A typical stratigraphic section through the BC given by Cawthorn (2006) is shown in
Figure 2-2. The mineralisation of interest with regard to platinum reserves is
contained in the Upper Critical zone of the BC.
Figure 2–2: Typical stratigraphy of the Bushveld Complex
The following extract from an unpublished report describes the mineral composition
of the Lower, Middle and Upper Groups of the BC. “Locally up to 25 chromicise
seams have been recorded, but 13 are regionally persistent. These are shown in
Figure 2-3 and are subdivided into Lower (LG), Middle (MG) and Upper (UG) groups.
The main Cr production in both the eastern and western Bushveld comes from the
LG6 seam, which averages about 1 m in thickness but can widen to 2.5 m. The
LG6A seam, 0.3 m thick, occurs in the hanging wall and is separated from the LG6
by a 0.8 m pyroxenite layer with disseminated chromites. As a result of the good
parting at the contacts of the LG6A and the weak friable nature of the pyroxenite in
places, the two reefs sometimes have to be mined together to a mining width of
Effect of time on the tensile strength of several Bushveld Complex rock types
11
approximately 1.8m. The LG6 seam typically comprises 97% chromite with an
average Cr/Fe ratio of 1.6 and Cr2O3 content of 46%, the quality being slightly better
in the Eastern Bushveld. The Middle Group comprises four horizons but each
horizon may consist of more than one seam. They occur within a stratigraphic
interval of 30 m to 50 m in both the eastern and western Bushveld. The lower two
seams (MG1 and MG2) occur in pyroxenite (Lower Critical Zone) host rocks, while
the MG3 and MG4 accumulated within norites and anorthosites which places them in
the Upper Critical Zone” (Rangasamy, 2010).
Figure 2-3: Lithographic representation of the Bushveld Complex (Rangasamy, 2010)
The Bushveld Complex is made up of several zones; the most important of which is
the Critical zone. “The Upper Group comprises two chromicise seams. The lower
UG1 seam, although up to a metre in thickness, has never been mined. The upper
UG2 seam is extensively mined for its platinum group element (PGE) content. The
quality of the chromite did not until recently allow its exploitation as a by-product. The
Effect of time on the tensile strength of several Bushveld Complex rock types
12
Merensky reef is the basal layer of a classic cyclic unit, which grades upwards from
pyroxenite to an anorthosite. Overlying the anorthosite is the Bastard reef, which
also forms the base of a cyclic unit terminating in the ‘giant mottled anorthosite’,
which is taken as the top of the Critical Zone. The reef can, from its normal
stratigraphic position where it conformably overlies the full succession of FW strata
in an area, abruptly or gradually transgress its FW to form local ‘potholes’ commonly
100 m2 to 30000 m2 in area, or even regions of pothole reef several km2 in extent.
Potholes interrupt the reef, appear unexpectedly and unpredictably and range in size
from 1 m to greater than 500 m in diameter” (Lomberg et al, 1999). Based on
regional changes in geological characteristics, the Merensky reef is divided into two
facies: the Rustenburg facies to the south of the Pilanesberg intrusion and the
Swartklip facies to the north. “The reef in its most common form is a pegmatoidal
(coarse-grained) feldspathic pyroxenite generally bounded by thin (approx. 20 mm)
chromicise layers. The immediate hanging wall is pyroxenite, 1 - 5 m thick which
grades upwards through norites to anorthosites. The FW generally comprises
various types of norite and anorthosite, and less commonly feldspathic pyroxenite or
harzburgite, which however often forms the immediate FW of pothole reefs”
(Rangasamy, 2010).
Egerton (2004) gives the middling between the Merensky reef and the UG2 reef
ranging between 12 m and 400 m, with sections of the BC where the two reefs
merge and can be mined together, the most common scenario being multiple reef
extraction. According to a study of Impala Platinum Mines’ 18 Shaft project contained
in an unpublished geotechnical report by Rangasamy (2010), “The average depths
of intersection below natural ground level for the reefs are 1391 m for the Merensky
(MR) bottom reef contact (BRC) and 1448 m for the UG2 top reef contact (TRC). The
shallowest reef contacts are 1048 m for the MR and 1093 m for the UG2 reef”. The
deepest reef contacts were given as 1881 m and 1964 m, for the MR and UG2
respectively in that particular project set up. The separation between the two mining
horizons was reported as 20.56 m (minimum) and 105.64 m (maximum), with an
average of 60 m. A gentle reef dip of 9 - 14˚ prevailed in the area covered in the
report. A schematic cross section of the upper portion of the Upper Critical Zone of
the Rustenburg Layered Complex, at Northam Platinum Mine, is shown in (Figure 2-
4).
Effect of time on the tensile strength of several Bushveld Complex rock types
13
Figure 2-4: Schematic cross-section of the upper portion of the Upper Critical Zone of the Rustenburg Layered Suite, at Northam Platinum Mine (Smith and Basson, 2006)
Occurrences of potholes, faults and dykes in the Merensky and Upper Group 2 reefs
disrupt the otherwise uniform dipping, shallow dipping and narrow tabular reef
characteristics peculiar to the Bushveld Complex mines. Geological losses of
between 20 and 25% have been reported by Egerton (2004) as a result of faults and
dykes intersected in the reef horizon.
2.1.3 The Bushveld Complex rock types
“Characteristics of the Critical Zone are: chromicise seams; repeated cyclic units
comprising a lowermost pyroxenite layer usually with a basal chromicise layer
grading upwards through norites (melanorite, leuconorite into anorthosite and very
well developed layering” (Cameron and Desborough, 1964). “The uppermost unit of
the Upper Critical Zone is an anorthosite with large inter-cumulus pyroxene mottles.”
Effect of time on the tensile strength of several Bushveld Complex rock types
14
(Mitchell and Manthree, 2002). The focus of this discussion is a chemical and
physical description of anorthositic rock types which make up the bulk of the host
rock for the platinum reserves in the BC.
2.1.3.1 Anorthositic rock types in the Bushveld Complex
Rocks are different to metals in that they are non-homogeneous due to their granular
make-up (Mercer, 2006), comprising “...an aggregate of crystals and sometimes
amorphous particles of mineral or organic matter, with sizes in the range of
millimetres to centimetres. ... They are held together with various amounts of
cement. The grains can consist of different kinds of minerals with different
mechanical behaviour. On a larger scale rocks are mostly continuous and
homogeneous, but quite often joints, faults, bedding planes, or different strata
appear. The result is rocks do not behave homogeneously as metals usually do”
(Critescu and Hunsche, 1998).
Anorthosite rock type is predominant in the Bushveld Complex and platinum bearing
formations the world over (Barnes and Maier, 2002). “Most anorthosite rock type is
dated between 3200 Ma and 2500 Ma. It is considerably less abundant than either
basalt or granite, but the complexes in which it occurs are often immense.
Anorthosite rock is a type of igneous rock composed predominantly of calcium-rich
feldspar. Anorthosite consists of plagioclase and feldspar grains cemented together.
This aggregate makes anorthosite a brittle rock. The rock consists of 90% or more of
cumulus plagioclase, together with small amounts of ortho-pyroxene and/or augite.
Mottled anorthosite refers to anorthosite in which large areas of inter-cumulus ortho-
pyroxene and/or augite (from 10 mm diameter up to the diameter of tennis balls)
form dark mottles in a matrix of pure white or pale grey anorthosite. Spotted
anorthosite is anorthosite in which a small percentage of cumulus ortho-pyroxene
gives the effects of dark spots in the pale anorthosite matrix. All anorthosites found
on the earth consist of coarse crystals, but some from the moon are finely crystalline”
(Barnes and Maier, 2002). It is generally accepted that crystalline rocks are brittle,
therefore stronger under compression than they are under tensile stress, as
witnessed by tensile strength values that are a magnitude of up to 20% lower than
the corresponding compressive strength values.
Effect of time on the tensile strength of several Bushveld Complex rock types
15
2.2 Behaviour of rock under stress
In-situ or virgin stress determines the stress redistribution observed when
excavations are mined in rock (Mercer, 2006). It is important therefore to carry out in-
situ stress measurements and use the data in mine planning and design to help
predict the behaviour of wall rock in planned excavations. However, in-situ stress
measurements are both difficult and expensive to conduct, hence relatively few data
have been collected the world over.
2.2.1 In-situ stress conditions of the Bushveld Complex
Around the world different authors have provided in-situ stress data from their
investigations carried out in the field during projects. Stacey and Wesseloo (2004)
collected a database of in-situ stress measurements across South Africa and results
of this investigation relevant to the BC are summarised in Figure 2-5. Generally high
principal stress k-ratios (2.5 – 4) are experienced in the BC mines at shallow depth
levels. At greater depths of about 1000 m, the stress ratios are lower, in the region of
(1 - 1.5).
Effect of time on the tensile strength of several Bushveld Complex rock types
16
0
500
1000
1500
2000
2500
3000
0 1 2 3 4 5k1
Dep
th (
m)
_
0
500
1000
1500
2000
2500
3000
0 2 4 6 8 10 12k1
Dep
th (
m)
_
Carletonville
Klerksdorp
Coal fields
Rustenburg
k1 envelope
k3 envelope
Figure 2-5: Ratio of the principal horizontal stress to the principal vertical stress for South African mines, (after Stacey and Wesseloo, 2004).
Instability problems in inclined shafts and in dip oriented tunnels have resulted in the
Rustenburg mining environment due to the unique stress conditions as
demonstrated in Figure 2-6.
Effect of time on the tensile strength of several Bushveld Complex rock types
17
Figure 2-6: Stress induced failure in the roof of a dip oriented tunnel in a platinum mine, (Stacey and Wesseloo, 2004)
The platinum and chrome mines in the Bushveld Complex (BC) have a high
horizontal stress in the “strike” direction as evidenced by observed “gothic arches” in
tunnels and haulages oriented on dip. Sidewall and hanging wall slabbing has
however been observed in platinum mine excavations in orientations free of the
major horizontal principal stress influence. The mechanism of fracture propagation
therefore has to be investigated at shallow depth in BC mines.
2.2.2 Behaviour of intact rock under stress
Laboratory tests are usually low cost and quick methods widely used to investigate
the modes and mechanisms of failure of rock specimens under different loading
conditions. Various modes of failure and mechanisms of failure under stress have
been explored (Stacey and Yathavan, 2003). Fracture propagation in low stress,
shallow depth mining environments is investigated to explain the observations made
in wall rock of BC mine excavations.
Effect of time on the tensile strength of several Bushveld Complex rock types
18
2.2.2.1 Behaviour of rock under compression
Different failure mechanisms are observed in rock prescribed by the stress
conditions and the inherent strength (and deformities) of the rock type under
investigation. Research has been carried out on the behaviour of rock under
compression (Bieniawski, 1967; 1969; 1970; Ashby and Hallam, 1986; Halm and
Dragon, 1998; Betournay and Mitri, 2003; Drescher and Handley, 2003; Szwedzicki,
2006; and Li et al, 2010). Various modes of failure were proposed and are briefly
discussed here.
Failure modes in rock specimens
Ashby and Hallam (1986) gave failure models for a rock specimen under
compression, as shown in Figure 2-7. According to Ashby and Hallam (1986) and as
depicted in Figure 2-7, (a) and (d) show slabbing when one or few cracks propagate
parallel to the principal compression, (b) depicts failure by aggregation of cracks to
form a shear zone and (c) presents near homogeneous deformations by distributed
micro-cracking. There are many possible crack orientations and therefore no two
rock specimens from the same rock type are likely to fracture in the exact same
manner.
Figure 2-7: Failure modes in compression (Ashby and Hallam, 1986)
Effect of time on the tensile strength of several Bushveld Complex rock types
19
Ashby and Hallam (1986) described the failure process in rock as consisting of “the
growth of single cracks in a stable way up to a stage where the interaction of cracks
increases the stress intensity driving crack growth and leads to instability and final
failure”. Betournay and Mitri (2003) observed that samples tested uniaxially exhibited
nearly equal spalling from all sides prior to the shear failure of the centre portion. A
varying degree of rock spalling (which can be attributed to extension fractures)
parallel to the free face was observed in the biaxial tested samples. Szwedzicki
(2006) stated that under compression a rock specimen can fail under tension or
compression, or a combination of both. He suggested that in uniaxial compression
tests on cylindrical specimens, the highest value of UCS is found for a specimen that
fails under extension. This postulation should however not be taken to suggest that
wherever high UCS values are observed extension is involved, or vice versa, but it is
a sign of fracture propagation in the direction of principal stress.
Crack initiation and propagation in rock specimens
The Griffith theory on crack initiation and growth in rock explains extension of cracks
when energy higher than the granular molecular bond in the rock is supplied to a
crack tip (Bieniawski, 1967a). Griffith’s theory explains the existence of cracks and
initiation of fractures in rock, but does not explain the rate of propagation and
extension of fractures; neither does it predict the occurrence of fracture failure, (Hoek
and Bieniawski, 1965). Ashby and Hallam (1986) discovered that a critical stress
was required to initiate crack growth, dependent on the initial crack length and
orientation, the coefficient of friction and the stress state. Bieniawski (1967b) tested
the behaviour of a crack in a glass sample and showed that fracture initiation will
start once the shear movement of the crack faces results in stable extension of the
crack tip close to the initial crack. The condition of the crack surfaces with regard to
shear movements therefore plays a big role in the initiation of fracturing in a glass
specimen. Halm and Dragon (1998) postulated a meso-crack theory for crack growth
as shown in Figure 2-8. This illustrates the tendency of fracturing in rock parallel to
the direction of the applied stress.
Effect of time on the tensile strength of several Bushveld Complex rock types
20
Figure 2-8: Crack branching mode under compressive loading (Halm and Dragon, 1998)
Krausz et al (1988) proposed an energy based fracture kinetics of crack growth for
all materials. This concept, which deals with inter-atomic bond energies, is more
suitable to homogeneous material unlike rock, which is largely heterogeneous.
Bieniawski (1967a; 1969; 1970) investigated fracture mechanisms in rock
extensively. Bieniawski (1967a) stated that a direct relationship existed between the
stress applied and the extension of crack length in rock. This process is irreversible,
hence permanent or plastic behaviour is dominant in rock compared with the small
elastic portion represented in stress-strain plots.
Long term strength in rock
Bieniawski (1967a) gave four stages of fracture development in rock starting from
fracture initiation and culminating in failure. These can be stated as:
I crack closure (closing of cracks),
II fracture initiation (linear elastic deformation),
III critical energy release (stable fracture propagation)
IV strength failure when maximum strength is achieved (unstable fracture
propagation) and
V rupture (coalescence of cracks) [failure of the rock].
The transition point between stable fracture propagation and unstable fracture
propagation marks the “long term strength” of the rock specimen, Figure 2-9.
Effect of time on the tensile strength of several Bushveld Complex rock types
21
Figure 2-9: Mechanism of brittle fracture under multi-axial compression, Bieniawski, (1967a)
Volumetric strain is given as the sum of the three orthogonal principal strains;
Volumetric strain = ( 1 + 2 + 3) = ( 1 + 2 x 3) since 2 = 3 in a triaxial
test,
where 1, 2 and 3 are the major, intermediate and minor principal strain
respectively.
Of interest is the volumetric strain-stress plot whose turning point showed the “long
term strength” of a rock specimen in Bieniawski’s analysis. This point was depicted
by Bieniawski (1969) to be about 80% of the UCS of the specimen and could be
checked by plotting the volumetric strain-stress curve for the specimen tested under
uniaxial compression. The same stress level was observed within tests of the same
rock type and is attributed to the onset of unstable fracture propagation. At this point,
if the stress applied is kept constant, eventual rupture of the specimen will occur with
the passage of time. In both the volumetric strain vs axial stress and lateral strain vs
axial stress the departure from linearity marks the point of fracture initiation in the
rock specimen. However, this point is not the same for axial strain vs axial stress
plot.
Effect of time on the tensile strength of several Bushveld Complex rock types
22
Hooke’s constitutive laws
Rock under uniaxial compression follows the Hooke’s law constitutive behaviour
given by:
Where E = elastic or Young’s modulus, σ = stress and = strain.
In three dimensions, Hooke’s law is given by the following equations in strain-stress
terms:
ε1 = [σ1 – ν (σ2 + σ3)]/E ε2 = [σ2 – ν (σ1 + σ3)]/E ε3 = [σ3 – ν (σ1 + σ2)]/E
where σ1, σ2 and σ3 are major, intermédiate and minor principal stress respectively,
E is the Elastic modulus and ν is Poisson’s ratio.
The elastic modulus determines how much a rock specimen can deform under load
before failure occurs, or within the rock’s elastic range. The elastic modulus of rock is
therefore a consistent property for the rock type and for linear elastic behaviour can
be used to calculate typical failure strain values from stresses recorded at failure.
Effect of shape and size on the strength of rock specimens
The shape and size of rock specimen influences its strength and deformation
behaviour. The influence of the height-to-width ratio on the failure mode of
rectangular hard rock prisms loaded under uniaxial compression was studied by Li et
al (2010). They investigated the surface parallel slabbing observed in deep hard rock
mines by investigating the stress conditions required to initiate slabbing in hard
granite rock surfaces using rectangular specimens with a range of width-height
ratios. They found out that at a height-to-width ratio of 0.5 the failure mode in the
specimen changed from shear to slabbing. They gave a slabbing strength of 60% of
the uniaxial compressive strength for Iddefjord granite from Norway. This indicates
that when tangential stresses calculated in excavation boundaries exceed the
slabbing or spalling threshold then fracture of excavation walls may be expected.
Effect of time on the tensile strength of several Bushveld Complex rock types
23
2.2.2.2 Behaviour of rock under tension
Goodman (1989), Bieniawski (1989) and Okubo and Fukui (1996) carried out
extensive direct tensile strength tests on several rock types and made a comparison
of the behaviour of rock under compression and under tension. They found that
“crack extension occurs in tension, whereas in compression, consolidation and crack
extension simultaneously occur”. Diederichs (2002; 2007) and Diederichs et al
(2004) carried out research into tensile slabbing in hard rock. They compared the
long term strength curves from laboratory tests to the in-situ strength of hard rock.
Their conclusion was that the in-situ strength of hard rock was less than the long
term strength of laboratory samples at low confinement, and therefore slabbing may
occur under such stress conditions.
Bieniawski (1967c) investigated fracture mechanisms and long term strength in rock
under tension. He found that the fracture process of rock under compression and
direct tension were virtually the same except that, under tension, there is an absence
of crack closure, and durations of stable and unstable crack propagation processes
are shorter. From Bieniawski’s results for norite under compression, fracture initiation
occurred at 35% of the maximum load while in tension it occurred at 94.5% of the
maximum load. It was also shown that unstable fracture propagation occurred in
compression at 73% of the maximum load, while in tension it occurred at 96.5% of
the maximum load.
The Brazilian Indirect Tensile (BIT) strength test
Tensile strength can be measured through direct or indirect methods. In the early
stages, a cylindrical dog-bone shaped specimen was suggested for use in
minimizing the effects of gripping of ends (Brace, 1964; Brace and Tapponier, 1976
and Hoek, 1964) as shown in Figure 2-10a. However, such specimens are difficult
and expensive to prepare in rock. The preparation of these shaped specimens is not
suitable for all rocks, especially for laminated soft rocks or very brittle hard rocks,
which usually fail during specimen preparation. The Brazilian Indirect Tensile (BIT)
strength test set up was hence developed to overcome this difficulty.
The Brazilian Indirect Tensile (BIT) strength test set up is shown in Figure 2-10b.
This test involves using a cylindrical specimen of radius R and length l, where,
Effect of time on the tensile strength of several Bushveld Complex rock types
24
preferably, R>25 mm and l = R (ISRM, 1981). The specimen is aligned with its axis
horizontal and compressed to failure between two concave steel platens by a load P.
(b)
Figure 2-10: Tensile strength testing set up, a) The dog bone shaped specimen used in direct tensile strength tests (Ryder and Jager, 2002) and b) Brazilian disc set up used in indirect tensile strength tests
In the test an induced indirect tensile stress field acts across the loaded diameter
tending to split the loaded disc apart. The value of the induced indirect tensile stress
at failure can be calculated from:
3 = -
= -t
Where P = load applied across test specimen, R = radius of test specimen and l =
the thickness of the test specimen (Jaeger and Cook, 1979).
Mellor and Hawkes (1971) explain that while the Brazilian test, carried out on solid
rock discs, is particularly appealing because of its simplicity in specimen preparation,
it produces failure in a biaxial, rather than a uniaxial, stress field. However, the
Effect of time on the tensile strength of several Bushveld Complex rock types
25
results from BIT tests have been widely found to be comparable to typical tensile
strength values, and therefore the test is widely used to establish tensile strength
values in rock (Ryder and Jager, 2002). The Brazilian test has been used in
numerous applications in the past. The test has been used to test the elastic
properties of concrete by Hondros (1959), thin spray-on liner products (TSLs) and
shotcrete by Yilmaz (2010), the tensile strength of coal by Berenbaum and Brodie
(1959) and Evans (1961), and that of rocks by Berenbaum and Brodie (1959); Hobbs
(1964); Hudson et al (1972); Chen and Hsu (2001) and Wang et al (2004). Hondros
(1959) developed a method to measure the elastic modulus and Poisson’s ratio
using the Brazilian test, but Wang et al (2004) found that in this process additional
strain gauge measurements must be implemented for improved accuracy, making
the procedure tedious.
Tests carried out on anisotropic rock specimens have shown the Brazilian tensile
strength to be dependent on the angle between the planes of rock anisotropy and
the loading direction (Chen and Hsu, 2001). The rock types tested in the current
research showed no anisotropy or lamination as they are largely igneous, isotropic
and homogeneous, therefore anisotropy effects have been ignored here. Hudson et
al (1972) observed that when carrying out the Brazilian test it was imperative to
concentrate the stress at the centre of the specimen so that crack initiation was not
at the circumferential contacts of the loading platens. They discovered this when
they used flat platens on granite, Solenhofen limestone and Tennessee marble discs
and rings. During the unloading tests Hudson et al (1972) found out that failure
always initiated at the loading points for flat platens and at the boundary of the hole
on the loaded diameter when a load distributing device was employed. Jaeger and
Hoskins (1966) had suggested a 15° loading arc on marble specimens to correct the
situation encountered by Hudson et al (1972) and gave a true value of the tensile
strength of the rock disc. They unloaded the specimen at the first sign of failure and
observed that cracks initiated in the interior of the sample ‘as an extension fracture’
which propagated to the surface. For validity of Brazilian test results Wang et al
(2004) emphasised the need for crack initiation from the centre of the specimen and
not from the specimen periphery in the Brazilian test. They suggested that a loading
angle corresponding to the flat end width must be greater than a critical value of
Effect of time on the tensile strength of several Bushveld Complex rock types
26
(2α ≥ 20°). Curved platens were used in the current research following this argument
to ensure crack initiation at the disc centre.
2.2.3 Characteristics of rock failure
Rock naturally fails when the applied stress exceeds the strength of the rock.
Despite this fact, rock specimens have been observed to fracture or fail at stress
levels lower than their Uniaxial Compressive Strength (UCS) values. In dry
conditions, under uniaxial stress, minerals generally fail by fracture at some value of
stress without prior internal rearrangement of their atomic structure (Duncan, 1969).
Lockner et al (1992) stated that “when rock is subjected to low stress levels,
geometrically sharp cracks concentrate stress at their tips to such a degree that local
failure can occur at modest applied stress”. This geometrical enhancement of stress
is a fundamental notion in fracture mechanics and has been successfully used to
analyze the strength of materials. Brace (1964), Hoek and Beniawski (1964) and
Bieniawski (1967; 1969; 1970) proved that Griffith’s theory is a good basis for the
study of the fracture of hard rock. Griffith’s theory indicates that, even if low stress
loading conditions prevail, as long as the energy generated on cracks exceeds the
molecular bond energy, propagation will result, leading to eventual widespread
failure. As a result Griffith’s fracture criterion is expressed in terms of the uniaxial
tensile strength of the material, since the molecular cohesive strength is difficult to
determine by direct measurement.
2.2.3.1 Fracture development in rock at low stress
Stacey and Yathavan (2003) studied the initiation of fractures at low stress levels in
rock. Studies and data on tunnel fracturing due to induced stress provided by
Grimstad and Bhasin (1997) supported by findings of Myrvang et al (2000) showed
that stress induced failure occurs even when the maximum induced stresses are as
low as a quarter to half of the rock strength. Ortlepp (1997) observed rock bursts in
a sandstone roof of a shallow coal mine with a low horizontal stress of 2 to 3 MPa
and a k–ratio of between 3 and 4. These findings further support the existence of low
stress fracturing in underground mining and construction and point to the fact that,
“the understanding of the mechanism of fracture initiation is essential for the correct
design of underground excavations” (Bieniawski, 1967). Brace and Tapponier (1976)
Effect of time on the tensile strength of several Bushveld Complex rock types
27
observed new trans-granular cracks to form in Westerly granite specimens loaded
under biaxial compression at about 75% of the peak stress. These cracks started at
high angle interfaces of dissimilar minerals and rarely at inclined pre-existing shear
cracks. The nucleation of cracks theory is further supported by Reches and Lockner
(1994) in their Acoustic Emission (AE) testing of crack propagation in Westerly
granite. Investigating the time it takes for these phenomena to manifest themselves
under low stress loading in rock is important to giving more information on the time-
dependent tensile strength of rock.
2.2.3.2 The extension strain criterion
Several authors have observed face parallel slabbing or spalling at low confining
stress and pointed towards extension fracturing as a fracturing mechanism. An
extension strain criterion was proposed by Stacey (1981) to describe the fracture
process existing in excavation walls at low stress levels. Stacey commented that the
existence of tensile conditions in rock is not a pre-requisite for the existence of
extension strain, since extension may occur with all three principal stresses being
compressive. According to Stacey (1981), fracture of brittle rock will initiate when the
total extension strain in the rock exceeds a critical value which is characteristic of
that rock type. Expressed simply, fracture initiates when:
ε3 ≥ εcr
where εcr is the critical value of extension strain and ε3 is the minimum principal
(extension) strain.
Fractures were observed to form in planes normal to the direction of extension strain
which corresponds with the direction of minimum principal stress (the least
compressive principal stress). Stacey (1981) wrote an equation for this behaviour for
linear material based on their strength properties as follows:
ε3 =
σ3 – (σ1 + σ2)]
where ε3 is minimum principal strain, σ1, σ2 and σ3 are the principal stresses, E is the
Elastic modulus and is the Poisson’s ratio.
Effect of time on the tensile strength of several Bushveld Complex rock types
28
From this argument it was shown that if
σ3
then the strain induced will be an extension strain, possibly leading to fracture. The
negative values of extension strain, and the zones under this influence, can easily be
identified in numerical models representing typical excavations. A comparison of the
magnitude of critical extension values observed here with actual laboratory test
derived strains, obtained at tensile failure, may be used to confirm if fracture initiation
and propagation may be expected in the excavation wall material.
2.3 Time-dependent characteristics of rock
Stress fields in in-situ rock change due to various mining activities (Mercer, 2006).
When an excavation is mined, stress redistribution occurs around the opening
resulting in compression, (major principal stress, σ1) and sometimes tension (minor
principal stress, σ3) concentration in the rock. A change in the stress field can result
in significant deformations in a rock mass occurring over a relatively long period of
time, especially as a result of creep, both within the intact rock and on the structures
making up the rock mass as a whole. The long term strength of the rock mass is
therefore partly controlled by the time-dependent weakening of intact rock (Lajtai,
1990).
2.3.1 Time-dependent behaviour in rock
Studies were conducted of time-dependent behaviour of clay based rock intended for
use as underground repositories for waste and toxic chemicals, galleries and access
tunnels by D’Elia (1991), Bernier et al (2004), Blumling et al (2007) and Bonini
(2009), rock salt caverns by Brouard (1988), Hunsche (1988), Charpentier (1988)
and Bérest et al (2005), hard solid rock in compression by Bieniawski (1967c; 1970),
Kovács (1971), Drescher (2002), Drescher and Handley (2003), Li et al (2010) and
Zhao et al (2011), granular material by Wang (2011) and rock masses in slopes for
open pit operations by Mercer (2006). Brittle materials are known to show the effect
of delayed fracture or static fatigue, which is defined as “a fracture, which occurs
after the elapse of time under a constant stress” (Salganik et al, 1994). These cover
diverse aspects of time-dependent behaviour in rock. An attempt is made here to
Effect of time on the tensile strength of several Bushveld Complex rock types
29
distinguish between creep behaviour in intact rock specimens and rheological
behaviour in rock masses.
2.3.1.1 Creep behaviour in intact rock
Creep is defined as increasing strain while the stress is held constant (Rinne, 2008).
Bieniawski (1970) states three basic time-dependent cases that can be investigated
namely:
(i) gradually increasing compression at different but constant rates of
deformation,
(ii) gradually increasing compression at varying rates of deformation and
(iii) constant load application for various time durations.
Creep is observed mainly in soft rocks like salt, coal and more or less in all other
rocks. However all types of hard rock also exhibit creep characteristics with long
enough time intervals (Critescu and Hunsche, 1998). Creep consists of three stages
according to Yu (1998) “... the first stage is instantaneous elastic strain when a
constant load is applied. If the load is sustained longer or the stress level increases,
then primary (transient) creep or attenuating creep occurs. At high stress, secondary
creep or steady state creep occurs. If the applied stress approaches or passes the
yield limit or the material strength, the strain will increase rapidly and a tertiary creep
or accelerating creep will appear and lead to eventual failure of the specimen.” The
tertiary stage always terminates in fracture and establishes the link with the
phenomenon of time-dependent failure (Wawersik, 1972). Figure 2-11 shows the
stages of creep in rock.
Effect of time on the tensile strength of several Bushveld Complex rock types
30
Figure 2-11: Creep curve showing different stages of deformation of rocks (Dubey and Gairola, 2008)
Drescher and Handley (2003) also observed the same creep stages when they
carried out uniaxial compression creep tests on Ventersdorp lava and Elsburg
Quartzite. They used the CSIR creep testing machine schematically illustrated in
Figure 2-12.
Figure 2-12: Principle of operation of the CSIR creep testing machine (Drescher and Handley, 2003)
Zhao et al (2011) carried out creep tests on red sandstone under uniaxial
compression and tension. They observed that under low stress levels the creep
Effect of time on the tensile strength of several Bushveld Complex rock types
31
curve of sandstone consisted of decay and steady state creep while the accelerated
creep stage typical of brittle fracturing was observed under high stress levels.
Long term creep tests done by servo-controlled testing machines have been found to
be expensive and prone to loading history effects (Li and Xia, 1999). A creep test on
potash salt rocks from Saskatchewan lasted from 2 to 8 months at a given load, with
most tests conducted over a 4-month period (Duncan and Lajtai, 1993). Watson et al
(2009) conducted creep tests on an anorthosite rock specimen with the Wits MTS
machine using triaxial loading with an axial loading of 72 MPa and a confining stress
of 1 MPa and the test lasted 3 hours. This explains the scarcity of research data from
creep tests especially on BC rock types.
Kranz (1976) investigated crack growth in loaded granite using an SEM (Scanning
Electron Microscope) and concluded that new cracks developed continuously under
constant load. Schimdtke and Lajtai (1985) observed time-to-fracture for granite and
anorthosite rock types through load-hold tests, with the result that stresses as low as
50% of the short-term strength (standard laboratory determinations) almost certainly
caused time-dependent stress corrosion cracking in brittle rocks severe enough to
cause delayed failure. Fabre and Pellet (2006) conducted strain creep tests on
clayey Tournemire argillite rock in France. Strain or deformation characteristics were
plotted against time, showing a linear behaviour with time on all strain levels. These
findings point towards the importance of including time-dependent behaviour in the
design of excavations in rock.
Creep is primarily influenced by stress level, temperature, humidity and chemical
action or environment (Jaeger and Cook, 1979; Malan, 1998 and Bérest et al, 2005).
Bérest et al (2005) used small dead weights (equivalent to a stress σ ≈ 0.02 - 3 MPa)
on top of rock salt in tests in an effort to keep “the applied stress as constant as
possible”, and the tests lasted “several hundreds of days” (650 days for rock salt
samples and 150 to 200 days for argillite samples). In these tests there was great
concern regarding the influence of the local environment over time. They observed
that “the behaviour of salt under small stress (σ ≈ 0.1 MPa) exhibits the same
general features as observed under larger stresses (σ ≈ 5 - 20 MPa).
Effect of time on the tensile strength of several Bushveld Complex rock types
32
Secondary creep has been proved to lead to failure for stresses as much as 30%
below the tested laboratory strengths, i.e. the long term strength of rock can be as
low as 70% of the Unconfined Compressive Strength (UCS) (Ryder and Jager,
2002). Dubey and Gairola (2008) used uniaxial compression (UCS) tests to test the
effects of anisotropy on rocksalt. They used constant stress loading levels of (30%,
40%, 50%, 60%, 70%, 72%, 75% and 80%) of the rocksalt’s uniaxial compressive
strength (failure stress or peak stress) to conduct creep tests. They also found out
that at higher stress loading levels structural anisotropy was insignificant to the creep
results.
2.3.1.2 Rheological characteristics of rock masses
Rheological behaviour in rock comprises of the effects of discontinuities like faults
and joints together with the time-dependent deterioration of intact rock. Closure
observed in the backs of stopes in deep mines can be easily attributed to rheological
behaviour of the rock mass. In less competent rock, time-dependent processes have
the benefit of dissipating strain energy in a non-violent fashion, whereas highly
stressed mining areas in competent rock are prone to strata bursting due to little
time-dependent behaviour (Brady and Brown, 1985).
Fakhimi and Fairhurst (1994) indicated that excavation “stand-up time” may run
typically between “minutes to years” depending on the rock mass involved. They
developed a mechanistic model for intact rock which incorporates time-dependent
deterioration of the rock strength with time for prediction of stand-up time of rock
structures. Excavations made in rock often assume “pseudo-stability” immediately
after mining and may stand for years to several decades before failure occurs due to
time-dependent deformation (Blumling et al, 2007 and Pellet et al, 2009). Figure 2-13
shows extension fracturing in an unsupported clay tunnel studied by Blumling et al
(2007). They studied the extension of the excavation damage zone (EDZ) in a tunnel
left unsupported after excavation.
Effect of time on the tensile strength of several Bushveld Complex rock types
33
Figure 2-13: Extension fracturing in an unsupported clay tunnel (Blumling et al, 2007)
Similar conditions are extrapolated to exist in hard rock types with the passage of
longer periods of time than is observed in the softer rock types investigated by
Blumling et al (2007). The argument here is that if excavations, especially ones in
soft rock, are left to stand for long enough periods of time, creep effects will lead to
integrity loss and eventual failure due to strength decay. Malan et al (2007)
investigated stope closure in an intermediate depth Merensky Reef stope 1400 m
below surface. Despite the mine being in brittle hard rock they observed time-
dependent creep behaviour as illustrated in Figures 2-14 and 2-15. The data was
recorded by a closure station at a fixed location in a panel and, with time, the face
moved away from the measurement point due to regular blasting. Interpretation is
difficult since the curves include both changes in face position and the time-
dependent deformation of the rock.
Effect of time on the tensile strength of several Bushveld Complex rock types
34
Figure 2-14: Time-dependent stope creep closure (Malan et al, 2007)
In between blasting times the steady time-dependent closure cycles were clearly
repeated during the recordings. These observations illustrated the combination of
time-dependent behaviour in the intact rock forming the rock mass and rheological
behaviour of the rock mass.
Figure 2-15: Continuous stope closure after blasting and the definition of closure terms, (Malan et al, 2007)
2.4 Summary and conclusions
The literature survey has shown the BC mining environment as consisting largely of
narrow tabular, uniform and shallow dipping reefs occasionally disturbed by
Effect of time on the tensile strength of several Bushveld Complex rock types
35
geological structures such as faults, dykes and potholes. High k-ratios prevail in the
BC with higher horizontal stresses than vertical stresses oriented along the strike of
BC rock strata. In these stress conditions excavation walls are often under low
compressive stresses and sometimes under tensile stresses. More importantly, the
brittle nature of BC rock types, particularly anorthositic rock types, was revealed.
Several modes of failure and fracture stages in brittle rock were discussed, with a
common fact that rock has inherent discontinuities (flaws) that extend and coalesce
when the energy from applied stress exceeds the molecular bond between rock
grains and surrounding matrix resulting in accelerated fracture propagation and
failure. The extension strain criterion was reviewed as a methodology adopted in this
research to investigate the onset of fracturing in rock. A study of brittle fracture
propagation at low stress revealed the time-dependent nature of rock under stress.
Creep activities were found by Jager and Ryder (2002) to be more pronounced close
to the exposed excavation walls, where the deviatoric stresses are large, coupled
with low confining stresses. Overall the review of literature illustrates that there have
not been many long term or creep strength tests in rock around the world, as the
methods are time consuming and therefore expensive. In South Africa, there have
been very few such tests carried out, the work by Drescher (2002) and Kovács
(1971) being notable exceptions.
Laboratory rock strength test methods were reviewed, with the UCS, normal and
time-dependent BIT strength tests being adopted for this research. The analysis of
volumetric strain to establish the long term strength of rock, used by Bieniawski
(1967; 1969; 1970), was adopted in this research with UCS tests. The long term
compressive strength of rock has been found from the current review to range
between 60% and 80% of the UCS of the rock type. Fracture propagation in rock
was shown to lead to deterioration of excavation walls with potential damage to life
of mine excavations. Fracture propagation in norite rock types has been shown to
initiate at 35% of the peak compressive load and 94% of the peak tensile load. A
background is thus set for the investigation of deformational characteristics of
several BC rock types.
Effect of time on the tensile strength of several Bushveld Complex rock types
36
CHAPTER 3
STRESS AND STRAIN ANALYSIS
3.1 Introduction
The Bushveld Complex (BC) mining environment, in-situ stress data, laboratory
strength test methods and deformational characteristics of rock under different stress
conditions were reviewed in the previous chapter. A brief description of the mining
methods used to exploit the narrow tabular PGM-rich reefs of the BC and the
analysis of stress and strain around typical excavations follows. The objective of this
chapter is to illustrate stress and extension strain scenarios that might be conducive
to the initiation and propagation of fractures around openings, using generic models
based on the characteristic BC mining geometry. Implications for the behaviour of
BC rock types hosting life of mine excavations under tensile stress or low
compressive stress (i.e., stress conditions that are prevalent in the BC mining
environment) are discussed here.
3.1.1 Mining methods used in the Bushveld Complex
Depending on the depth of operation and geology, conventional and/or mechanised
methods are utilised to exploit narrow reef ores of the Bushveld Complex.
Conventional mining methods commonly, but not exclusively, use track bound
equipment, while trackless equipment is largely, but not exclusively utilised in
mechanised mining operations. With reference to Chapter 2, where the BC geology
was discussed, the reefs from which PGM ores are mined are largely of uniform
width and constant gradient, disturbed occasionally by the intersection of dykes and
by reef rolls caused by the intersection of potholes.
3.1.1.1 Conventional mining methods
Conventional mining methods are commonly used to extract narrow tabular reefs like
the Merensky, UG2 and several gold bearing reefs of the Witwatersrand basin. The
reef is extracted from uniform width stopes using handheld jack hammers to drill
Effect of time on the tensile strength of several Bushveld Complex rock types
37
charge holes, and panel faces are subsequently blasted. Broken ore is transported
out of the stopes by scraper winches acting down dip at the stope face, and then
along strike oriented gullies in the reef footwall (FW) waste. Complete reef extraction
is not possible since in-stope and regional stability pillars are left in-situ to maintain
the excavations open and reduce the size of exposed hanging wall (HW) span, thus
decreasing the height of the tensile zone. A typical conventional breast mining layout
described by Egerton (2004) is shown in Figure 3-1. Up-dip and down-dip mining are
variations of the conventional mining method with different mining advance
directions.
Figure 3-1: Conventional breast mining layout in the UG2 reef (after Egerton, 2004)
Smith and Basson (2006) refer to the existence of potholes left in-situ as pillars in the
Merensky reef mining stopes. Potholes may not be mined because they are often
associated with heavy jointing in the rock mass, and the resultant footwall horizon is
not amenable with ore cleaning operations using scraper winches. Pillars left in the
Effect of time on the tensile strength of several Bushveld Complex rock types
38
Merensky reef horizon may induce elevated stresses on the footwall excavations,
including the UG2 mining stopes at deeper levels beneath the Merensky reef.
3.1.1.2 Mechanised mining methods
Room and pillar mining layouts are used to mine uniform shallow-dip, continuous
reef at shallow depth using mechanised equipment. Most development is on reef
with roadways and split holings made between pillars to afford access to machinery
and equipment. The split holings also serve for ventilation purposes. Room and pillar
mining methods have become equally popular in the Bushveld Complex mines as
conventional mining methods, particularly at shallow mining depth. Hybrid room and
pillar mining methods have also been tried in the BC platinum mines. A typical room
and pillar operation is shown in Figure 3-2.
Figure 3-2: A typical room and pillar mining layout (after Egerton, 2004)
Roof bolters install mechanical bolts and/ or resin bolts in the hanging wall in the
rooms. There are several variations to the mechanised room and pillar mining
Effect of time on the tensile strength of several Bushveld Complex rock types
39
method, as described by Egerton (2004). Pillars in this mining set up are often
square and cut to remain stable within their elastic limit. The geometry common to
conventional and mechanised mining methods is the creation of shallow dipping
uniform height excavations with pillars left in-situ. The life of mine access
excavations and pillars mined in these mining methods have been observed to be
subject to time-dependent deformations.
3.2 Characteristic geometries of Bushveld Complex mine excavations
Theoretical mining geometries based on typical BC mine excavations were used in
this research and are briefly discussed here. Generic models were used to analyse
stress and extension strain using a 2-D (2-Dimensional) commercial software
package (Phase2) for the purposes of illustrating characteristic stress distributions
and illustrate susceptibility to the initiation of fractures around modelled excavations.
3.2.1 Geometries of an in-stope pillar
2-D analyses were used as they suffice to indicate the stress and strain distributions
expected around the excavation assuming uniformity and continuity in the out of
plane direction with the resulting model shown in Figure 3-3.
Figure 3-3: Modelling geometry of a 6 m wide by 1.8 m high in-stope pillar
In conventional mining methods, in-stope strike pillars are designed to crush on
cutting and to operate in their post peak state utilising their residual strength. The
Effect of time on the tensile strength of several Bushveld Complex rock types
40
criterion based on a width to height ratio not exceeding 3 and a Factor of Safety
(FOS) < 1. Width to height ratios are typically 2 – 2.5 and in stoping widths of 1.2 -
1.75 m, typical crush pillars are 2.4 – 3.5 m wide. These pillars can be dip or strike
oriented. Panel spans here are determined by the height of the tensile zone, mining
depth or the use of the elastic beam theory to determine stable spans between
pillars. In room and pillar mining elastic pillars loaded below their peak strength with
a Factor of Safety (FOS) > 1.5 are cut in a uniform array, often based on square
shaped pillars. The width to height ratio for these pillars must be greater than 5. The
aim is to achieve profitable extraction ratios from several combinations of pillar and
room sizes complying with the requirements of the pillar geometry and strength
criterion applied. Characteristic pillar sizes in room and pillar mining are 5 -10 m with
6 – 12 m rooms.
3.2.2 Geometries of a mining stope
Panel spans are typically 15 – 40 m long where conventional mining methods are
used whilst 6 – 12 m is the room span typically mined in room and pillar mining
methods, with pillars cut on a systematic array. The geometry of a 29 m long panel
with a 1.8 m stope width is depicted in Figure 3-4.
Figure 3-4: Modelling geometries of a 29 m by 1.8 m high stope
Effect of time on the tensile strength of several Bushveld Complex rock types
41
3.2.3 Geometries of an incline shaft
Roadways and declines are typically 3 – 8 m wide and 1.8 – 4 m high. A 7 m wide by
4 m high shallow dipping incline is represented in Figure 3-5.
Figure 3-5: Modelling geometry of a 7 m wide by 4 m high incline shaft
Continuum and elastic assumptions were made, and analyses were carried out using
the assumption of plane strain conditions where the out of plane strain is assumed to
be zero or very negligible. A uniform geometry of the models is assumed to continue
infinitely in the out of plane direction. The dimensions of the excavations represented
in the models are indicated in Figures 3-3 to 3-5. Note that the models discussed
here represent typical excavations mined in BC mines.
3.3 Numerical and analytical methods
Direct methods of investigating in-situ behaviour of rock are not always available or
practical and as a result researchers turn to numerical methods and laboratory tests
on rock to determine trends and behaviour of rock masses under different stress
conditions. The use of numerical modelling to analyse the time-dependent behaviour
of rock under different loading conditions in excavations made in soft and hard rock
is reviewed here.
Effect of time on the tensile strength of several Bushveld Complex rock types
42
3.3.1 Review of numerical methods in mining
Numerical modelling can be used to investigate the behaviour of rock around
excavations otherwise difficult to measure in-situ to put observed and laboratory test
results into the practical context of typical mine excavations. Time-dependent
numerical modelling for underground excavations has been performed by Boidy et al
(2002), Bonini et al (2009) and Pellet et al (2009). Boidy et al (2002) used Lemaitre’s
visco-plastic model to simulate the time-dependent behaviour of a tunnel in
Switzerland. Confirmation of propagation of the damage zone with the progression of
time through numerical analysis was illustrated by the work done by Bonini et al
(2009). They proved that clay shales exhibited time-dependent behaviour both at
laboratory and tunnel level, Figure 3-6.
Figure 3-6: Extension of damaged zone for different time progressions in a section located 6 m behind the tunnel face (Bonini et al, 2009)
In conclusion of their studies on clay shale, Bonini et al (2009) found that parameters
determined from laboratory tests could not always be directly used for appropriate
prediction of tunnel behaviour. This was mainly because of the complications
introduced by water content, swelling or squeezing, fracturing and jointing, effects
Effect of time on the tensile strength of several Bushveld Complex rock types
43
which might not be present in a laboratory size specimen. Pellet et al (2009) used
the Lemaitre visco-elastic damageable model to calculate strains with respect to time
as well as time to failure. They confirmed the extension of the damage zone inwards
from the excavation walls with the passage of time. They showed that it is possible to
assess the time-dependent changes in the extension of the Excavation Damage
Zone (EDZ) induced in front of the work face.
In the current research, 2-D numerical analysis was used to determine stress and
strain distributions around typical BC mine excavations and to illustrate zones
around the excavations where the extension strains occur.
3.3.2 Stress-strain analysis objectives
Anderson (1951) indicated that establishing in-situ stress conditions in underground
mining is difficult. According to Anderson’s concept in ideal ‘standard state’
conditions the lateral stress state should equal the vertical stress as depth increases.
It is also difficult and expensive to establish induced stress conditions by direct
measurement. The behaviour of rock under stress is therefore determined through
monitoring other physical quantities like strain, or through numerical modelling of
excavations (Pollard et al, 2005). Elastic plane strain, 2-Dimensional numerical
modelling was used to investigate the distribution of stress and strain around typical
Bushveld Complex mine excavations. The objectives of the numerical analysis are:
To illustrate the distribution of elastic stress (compressive major σ1 and minor
σ3 principal stresses) around three typical Bushveld Complex excavations;
To illustrate characteristic distributions of extension strains around typical
Bushveld Complex mine excavations, and to compare their magnitudes with
typical strain values obtained at tensile failure in laboratory indirect tensile
strength tests, and;
To interpret the results from the numerical analyses in relation to the observed
underground behaviour of the rock surrounding the excavations.
The geological characterisation and description of typical mining geometries given in
preceding sections was used as a basis for the models used here.
Effect of time on the tensile strength of several Bushveld Complex rock types
44
3.3.3 Methodology for stress and extension strain analysis
Numerical analysis was achieved by:
Investigating the distribution of stress (major principal stress, σ1 and minor
principal stress, σ3) around the following excavation models (see also section
3.2);
A 6 m wide in-stope dip pillar in a 1.8 m high stope width, Figure 3-3;
A typical 29 m long stope in a 1.8 m high stope width, Figure 3-4 and
A 7 m x 4 m decline shaft, Figure 3-5.
Illustrating the distribution of extension strain around the modeled excavations
with emphasis on:
Depicting the characteristic magnitudes and orientations of extension
strains in the excavation peripheries and at various locations around
the excavations.
Depicting the zones around the model excavations where potential
initiation of fractures might occur (i.e. zones of critical extension strain).
Comparing the calculated extension strain values with the strain values
observed at tensile failure in the laboratory tests conducted on several
BC rock types.
Drawing potential parallels between the modeling results and the
observed failure behaviour in BC mine excavation wall rock and
characteristic failure modes observed in compressive and indirect
tensile strength tests.
Average properties of the several anorthositic rock types (reported in Chapter 4)
were used to assign rock strength and deformational properties to the models.
3.4 Stress and extension strain analysis
Stress and extension strain were determined at different depths for two k-ratios: a k-
ratio of 2, characteristic of the shallow BC mining environment (Stacey and
Wesseloo, 2004), and a k-ratio of 1 representing theoretical hydrostatic loading
conditions more typical of the deeper mines. The models were analysed for two
depths of 500m and 1000m below surface. The overburden unit weight was taken as
Effect of time on the tensile strength of several Bushveld Complex rock types
45
29 kN/m3, derived from the average density of several Bushveld Complex rock types
determined in laboratory testing (see Chapter 4). The further aim of the analyses
was to illustrate the locations of high stresses, and the extents of tensile zones and
zones of extension strain around typical BC mine excavations that could promote
fracture initiation, fracture propagation and spalling in anorthositic rock types.
3.4.1 Analysis of results - in-stope pillar model
Results of the computation of the major principal stress (σ1), minor principal stress
(σ3) and extension strain around a typical in-stope pillar model are depicted in Figure
3-7 to Figure 3-12.
3.4.1.1 Major Principal Stress
The major principal stress distribution around an in-stope pillar model is depicted in
Figures 3-7 to 3-10 for two different loading conditions and two different depths
below surface.
σ1 contours: Depth = 500 m and k = 1
Figure 3-7: Distribution of Major Principal Stress (σ1) at a depth of 500m with a k-ratio = 1
Effect of time on the tensile strength of several Bushveld Complex rock types
46
σ1 contours: Depth = 500 m and k = 2
Figure 3-8: Distribution of Major Principal Stress (σ1) at a depth of 500m with a k-ratio = 2
σ1 contours: Depth = 1000 m and k = 1
Figure 3-9: Distribution of Major Principal Stress (σ1) at a depth of 1000m with a k-ratio = 1
Effect of time on the tensile strength of several Bushveld Complex rock types
47
σ1 contours: Depth = 1000 m and k = 2
Figure 3-10: Distribution of Major Principal Stress (σ1) at a depth of 1000m with a k-ratio = 2
The results of the analysis of major principal stress show that at a depth of 500 m for
both k-ratios 1 and 2 low compressive stresses (5 – 7.5 MPa) are observed in the
HW and parts of the pillar sidewall (blue to light blue in the models). At the pillar
apexes stress concentrations, illustrated by elevated stresses (25 – 35 MPa), are
observed. At a simulated depth of 1000 m and k-ratio = 2, lower major principal
stress values (0 – 4 MPa) are observed in the hanging wall of the excavation. At the
pillar cores intermediate stress conditions (27.5 – 44 MPa) are observed. The
orientation of the major principal stress contours in all cases is parallel to the
excavation walls (hanging, foot and sidewalls – HW, FW and SW). The major
principal compressive stress values observed in the immediate walls of the
excavation are up to 10 times lower than the compressive strengths of the BC rock
types. The compressive strength of the BC rock types are discussed in Chapter 4.
3.4.1.2 Minor Principal Stress
The minor principal stress (σ3) was computed and its distribution around the
modelled excavation is presented in Figures 3-11 to 3-14.
Effect of time on the tensile strength of several Bushveld Complex rock types
48
σ3 contours: Depth = 500m and k = 1
Figure 3-11: Distribution of Minor Principal Stress (σ3) at a depth of 500m with a k-ratio = 1
σ3 contours: Depth = 500m and k = 2
Figure 3-12: Distribution of Minor Principal Stress (σ3) at a depth of 500m with a k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
49
σ3 contours: Depth = 1000m and k = 1
Figure 3-13: Distribution of Minor Principal Stress (σ3) at a depth of 1000m with a k-ratio = 1
σ3 contours: Depth = 1000m and k = 2
Figure 3-14: Distribution of Minor Principal Stress (σ3) at a depth of 1000m with a k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
50
Very low stress (0 to 2 MPa) and negative minor principal stress (0 to -2 MPa) values
are observed in the immediate excavation walls (light blue to dark blue), implying
very low confinement to possibly tensile excavation wall conditions. The pillar core is
under moderate stress (23 – 27 MPa) implying moderate confining stress. Minor
principal stress depicted in Figure 3-12 ranges from (-1.5 to 3 MPa), much lower in
magnitude than the tensile strengths of Bushveld Complex rock types which have an
average tensile strength of 7.2 MPa. The orientation of minor principal stress
contours is parallel to the excavation wall surfaces in the HW and pillar SW and
resembles the orientations of fracture planes observed in the wall rock.
3.4.1.3 Extension strains
The evaluation of extension strains that follows was carried out to allow application
of the extension strain criterion proposed by Stacey (1981), see also section 2.2.3.2.
The strain equation
3 =
σ3 – (σ1 + σ2)]
was inserted into the user defined data analysis in the Phase2 programme to
compute the distribution of minimum principal strain around the modelled
excavations. Extension strains that exceed a critical extension strain value indicate
the initiation of fracturing in rock. It is to be noted that the value of σ2 used in the
analyses results from the plane strain assumption, and thus the calculated extension
strains are not completely correct. Nevertheless, they are adequate to indicate the
approximate magnitudes of extension strain in the rock surrounding typical BC
excavations. The distribution of extension strain around the pillar model is given in
Figure 3-15 and Figure 3-18.
The extension strain values depicted in Figure 3-15 range from -1.6 x 10-3 to 2.45 x
10-3 (blue to dark green) starting from the excavation wall surface to the interior core
of the pillar. In all four cases, the immediate peripheries of the excavations are
shown to experience negative extension strains, which indicate the potential initiation
of fracture in the rock.
Effect of time on the tensile strength of several Bushveld Complex rock types
51
Extension strain contours: Depth = 500m and k = 1
Figure 3-15: Distribution of extension strain at a depth of 500m with a k-ratio = 1
Extension strain contours: Depth = 500m and k = 2
Figure 3-16: Distribution of extension strain at a depth of 500m with a k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
52
Extension strain contours: Depth = 1000m and k = 1
Figure 3-17: Distribution of extension strain at a depth of 1000m with a k-ratio = 1
Extension strain contours: Depth = 1000m and k = 2
Figure 3-18: Distribution of extension strain at a depth of 1000m with a k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
53
An annotated picture of extension strain modelling is given in Figure 3-19 depicting
the zone of influence of critical extension strain with similar values to laboratory
tensile strains at failure.
Figure 3-19: Distribution of Critical Extension strain at a depth of 500 m and k = 2
Stacey (1981) stated that each rock type has a critical extension strain value at
which fracture propagation initiates. Depending on the stress loading conditions, the
critical strain value may be exceeded at some location on the boundary of the
excavation resulting in spalling of the rock material in that zone. With little
confinement at the rock wall surface and the intersection of natural geological
discontinuities, slabs of rock may fall out with time. The zones around the excavation
periphery where fractures could be expected to initiate are demarcated with arrows
in Figure 3-19. The magnitudes of extension strain depicted here are in the order of
1.05 x 10-3 and less, exceeding the calculated strain values at failure obtained from
laboratory indirect tensile strength test results of some 1.6 x 10-4, see chapter 4.
3.4.1.4 Excavation wall spalling observed underground
In the BC, in-stope pillars are cut in reef rock types which contain low strength and
brittle chrome seams alternating with pyroxenite and anorthositic rock type layers.
Failure in in-stope pillars may therefore manifest through the weak chrome seam
exacerbated by the layered nature of the Merensky and UG2 reefs. Although
observed hanging wall de-lamination has arguably been attributed to the layered
Zone of critical extension strain
with strain values similar to
laboratory tensile strains at
failure.
Effect of time on the tensile strength of several Bushveld Complex rock types
54
nature of the BC rocks, the direct effect of low confinement or tensile stress
conditions augmenting dilation or extension of the laminated HW is evident. The
models depicted zones of critical extension strain and principal stress contours with
orientations that are compatible with the spalling observed in the excavation wall
rock. Without quantifying the extent of fracturing or the depth of the fractured zones
around in-stope pillars, observations were made on pillars cut in the UG2 reef
horizon of a platinum mine.
The photographs that follow in Figures 3-20 to 3-22 were taken in platinum mine
stopes that had been standing for at least 6 months. The laminated beam in the
hanging wall of the stope de-laminated due to tensile dilation under the weight of the
beam. Face parallel fractures with the same orientation as the modelled principal
stress contours developed slowly at stresses lower than the compressive or tensile
strengths of the host rock types, Figure 3-21. Loose blocks form when the fractures
propagate and intersect natural discontinuities, resulting in unravelling around
support. Installed support in these conditions curbs the propagation of fractures, and
slows down the manifestation of excavation wall damage.
Figure 3-20: De-lamination of hanging wall strata
Effect of time on the tensile strength of several Bushveld Complex rock types
55
Figure 3-21: Hanging wall damage under tensile stresses in a stope
Spalling of the wall rock was also observed in a platinum mine haulage, Figure 3-22.
Annotations on the picture were made to illustrate spalling and the profile of the
haulage as the walls had been white-washed, obscuring the spalling.
Figure 3-22: Spalling parallel to the haulage walls induced by extension strain observed in a FW haulage mined in anorthositic norite
Effect of time on the tensile strength of several Bushveld Complex rock types
56
Modelling results for a stope and an incline shaft excavation are presented in
Appendix C and direct reference to these is made in the main content of this
research. To bring this analysis into the context of characteristic strains observed in
actual rock, a laboratory rock testing programme was conducted and the results are
presented in the next chapter. A comparison can therefore be made between strain
values observed in rock specimens at failure and modelled critical extension strains.
3.5 Conclusion
Fracture initiation and propagation mechanisms were investigated in Chapter 2,
showing that fracture propagation may take place even at low compressive stresses,
and even more so under tensile stress, with fractures often aligned parallel to the
direction of the principal stress contours. The potential for fracture development was
investigated through numerical modelling reported in Chapter 3. The models showed
that low confinement, and in some instances, tensile stress conditions, around
excavation peripheries may promote fracturing, slabbing and dilation of the
excavation walls. The results of the analyses demonstrated that very substantial
zones of extension strains, of significant magnitudes, occur around the boundaries of
BC excavations. The propagation of fractures commonly observed in excavations is
sub-parallel to the orientation of the excavation walls. In addition, fractures may
intersect pre-existing natural discontinuities, resulting in the formation of key blocks
with a potential to fall out from the excavation walls. Thus, investigation of the effect
of time on the behaviour of BC rock types under tensile stress and extension strain is
very important with regard to the long term stability of excavations in these rocks.
Effect of time on the tensile strength of several Bushveld Complex rock types
57
CHAPTER 4
LABORATORY TESTS ON BUSHVELD COMPLEX ROCKS
4.1 Introduction
The preceding chapters provided a background on the Bushveld Complex (BC)
mining environment, the characteristic mining methods used in the BC, the
behaviour of rock under different stress conditions and stress-strain analysis around
typical BC excavations. Laboratory rock strength tests have been carried out to
provide data for comparison with the behaviour of several BC rock types under
stress loading conditions in typical BC mine excavations presented in the previous
chapter. The current chapter reports the results of Uniaxial Compressive Strength
(UCS), and normal and time-dependent Brazilian Indirect Tensile (BIT) strength
tests.
4.1.1 Testing objectives
Laboratory rock strength tests were carried out on several Bushveld Complex (BC)
rock types to establish the following characteristics of the rock types under
compressive stress:
Elastic properties and failure characteristics under uniaxial compression
(UCS), the results of which were used as input for the numerical analysis of
stress-strain presented in the previous chapter.
Long term strength and stress-strain values observed at failure.
Indirect tensile strength characteristics and
Time-dependent behaviour under indirect tension.
These objectives were achieved using the methodology outlined in the following
section. All rock specimen preparation and testing was carried out in the Genmin
Rock Testing Laboratory at the University of the Witwatersrand.
Effect of time on the tensile strength of several Bushveld Complex rock types
58
4.1.2 Testing methodology
The following methodology was used to achieve the investigative objectives outlined
above:
Conducting:
UCS tests on cylindrical specimens of several BC rock types prepared
from different depth sections along a single, vertical drill hole core;
Normal BIT tests on Brazilian discs of several BC rock types, and
Time-dependent constant hold-load BIT tests on Brazilian discs of several
BC rock types stressed to pre-determined hold-load levels (90%, 85%,
80%, 75% and 70%) of the average tensile strength (σt) of the rock type,
i.e. load at failure from the normal BIT test. The times-to-failure for the
different test categories at constant load were recorded for time-dependent
analysis.
Processing, representing and analysing the recorded results.
4.1.3 Spatial location of core samples
The UCS and BIT test specimens were prepared from core of a single exploration
drill hole BH6082. The spatial location of the drill hole is given in Table 4-1.
Table 4-1: Exploration drill hole coordinates
Borehole
Identification
Co-ordinates
X Y Collar Z-value
BH6082 2823730.32 -28219.79 1122.51m AMSL
A full geological log sheet can be found in Table A1-1 in Appendix A. The vertical
borehole gives a good cross-sectional representation of the Bushveld Complex
stratigraphy. Drill hole core samples were taken from a depth up to 10m above and
below the hanging wall (HW) and footwall (FW) contacts of the Merensky (MR),
Upper Group 1 (UG1) and Upper Group 2 (UG2) reef horizons.
Effect of time on the tensile strength of several Bushveld Complex rock types
59
4.1.4 Distribution of test specimens
Several rock types were identified from the drill core which was used in the
preparation of cylindrical specimens for Uniaxial Compressive Strength (UCS) tests
and discs for Brazilian Indirect Tensile (BIT) strength tests.
The test specimens were given sample identities for easy referencing according to
rock type, lithographic placement (depth) and the test type carried out as shown in
Table 4-2.
Table 4-2: Specimen nomenclature
Rock type
Lithographic zone depth/
Rock type ID
code
UCS sample ID code
Normal BIT
sample ID code
Time-dependent
BIT sample ID
code From-To (m)
Mottled Anorthosite
(1637.54 – 1645.27)
A UCA NBA TB%A
Spotted Anorthositic
Norite
(1615.64 –1627.50)
B UCB NBB TB%B
Pyroxenite (1603.85 – 1610.05)
C UCC NBC TB%C
Mottled Anorthosite
(1600.07 – 1602.37)
D UCD NBD TB%D
Norite (1564.79 – 1566.92)
E UCE NBE TB%E
Spotted Anorthositic
Norite
(1561.45 - 1564.70)
F UCF NBF TB%F
Anorthositic Norite
(1557.30 - 1558.45)
G UCG NBG TB%G
Spotted Anorthosite
(1550.51 – 1557.30)
H UCH NBH TB%H
Mottled Anorhtosite
(1546.38 – 1550.51)
I UCI NBI TB%I
Nine test specimen categories were identified using this methodology and were
given alphabetical codes (A to I), starting from the deepest level hosting the Upper
Group 1 (UG1) rock types to the shallowest level hosting the Merensky (MR) rock
types. The nomenclature was completed by assigning short prefixes (UC, NB and
TB) representing uniaxial compression, normal Brazilian and time-dependent
Brazilian strength tests respectively. The rock types represented in the nine test
specimen categories are: spotted and mottled anorthosite, pyroxenite, norite,
Effect of time on the tensile strength of several Bushveld Complex rock types
60
anorthositic norite and spotted anothositic norite. UCS and BIT test specimens were
cut alternately from the core to give an unbiased sample representation for the two
test methods. No two test specimens for the same test method were cut adjacent to
each other. The distribution of prepared test specimens for the different test
specimen categories is given in Table 4-3.
Table 4-3: Distribution of test specimens
Reef profile
Rock type
Depth
Identity code
No. of specimen tested in UCS test
No. of specimen tested in Normal BIT test
No. of specimen tested in
Time-dependent
BIT test
No. of specimen per rock
type From - To
(m)
UG1 FW
Mottled Anorthosite
(M.A.)
(1637.54 – 1643.27)m
A 5 6 32 43
UG2 FW
Spotted Anorthositic
Norite (S.A.N.)
(1615.64 – 1627.50)m
B 5 8 44 57
UG2 HW
Pyroxenite (P.) (1603.85 – 1610.05)m
C 5 9 17 31
UG2 HW
Mottled Anorthosite
(M.A.)
(1600.07 - 1602.37)m
D 5 7 24 36
MR FW Norite (N) (1564.79 – 1566.92)m
E 5 7 11 23
MR FW Spotted
Anorthositic Norite (S.A.N.)
(1561.45 – 1564.70)m
F 5 7 17 29
MR HW Anorthositic Norite (A.N.)
(1557.30 – 1558.45)m
G 5 8 14 27
MR HW Spotted
Anorthosite (S.A.)
(1550.51 – 1557.30)m
H 5 8 35 48
MR HW Mottled
Anorthosite (M.A.)
(1546.38 – 1550.51)m
I 5 7 28 40
Total no. of specimens 45 67 222 334
The distribution of the test specimens is presented graphically in Figure 4-1.
Effect of time on the tensile strength of several Bushveld Complex rock types
61
Figure 4-1: Graphical presentation of the distribution of test specimen
The greatest numbers of test specimens were prepared for the BIT test, and most of
these were used in the time-dependent tests. For each test type, the numbers of
specimens that were tested successfully and gave valid results varied.
4.1.5 Preparation of test specimens
All specimens were prepared and tested according to the ISRM Suggested Methods
for rock testing (ISRM, 1981; 2007). The drill core samples were largely undisturbed,
intact and showed no signs of stress relief induced “discing” or high stress fracturing,
hence the test specimens were considered not to have visible pre-existing
deformities. All tests covered in this research were carried out in anhydrous
conditions at room temperature and pressure (r.t.p.). The sample width, height,
diameter and weight were measured and recorded after the samples were left to dry
naturally, to avoid the influence of moisture from the water used during specimen
cutting. The cores were BQ size with a diameter, D = 36.3 mm and were prepared to
yield specimens with a length-to-diameter ratio, L/D, of 2.2 – 3.0 for the UCS tests,
and a thickness-to-diameter ratio, t/D, of 0.4 - 0.6 for the Brazilian tests, Table 4-4.
An average width to height ratio of 2.2 and 0.5 for the UCS and BIT test specimens
respectively was achieved. Two shapes of specimen were used, as illustrated in
Figure 4-2.
0
10
20
30
40
50
A B C D E F G H I Test
typ
e N
o. o
f sp
ecim
en
s
Test category identity code
Distribution of test specimen UCS Test
Normal BITTest
Time-dependentBIT Test
Effect of time on the tensile strength of several Bushveld Complex rock types
62
Figure 4-2: Rock specimens for UCS and BIT test shapes
The specimens were cut parallel, ground and polished flat to remove all asperities
and undulations which could introduce non-uniform loading.
4.2 The UCS test set up
The Amsler conventional compression rock testing machine was used to carry out
UCS tests, Figure 4-3.
Figure 4-3: The Amsler testing machine
Effect of time on the tensile strength of several Bushveld Complex rock types
63
Strain gauges were attached in circumferential and axial directions on the UCS test
specimens to measure strain during the test. Lead wires from the gauges, and the
output from a load cell, were connected to a data recording and processing computer
to give strain and stress values, which were used to analyse the compressive
behaviour of the various rock types. The Amsler testing machine is a conventional
loading machine, and despite non-violent failure of many specimens on reaching
peak strength, not much information could be salvaged from the post-peak period of
the tests due to the recording limitations of the recording system and rupture of strain
gauges at specimen failure.
4.3 Analysis of UCS test results
A comprehensive UCS testing programme was conducted. Only a summary of the
UCS test results together with the long term strength analysis is presented here to
keep the write-up small and the analysis focused. The salient trends from the results
are presented here, and the full set of all results is contained in Appendix B1.
4.3.1 Processing of UCS test results
Detailed processing of one UCA test category is presented here together with stress-
strain plots. A full set of the UCS results for all the test categories, and
representative stress-strain plots, are contained in Appendix B1. Recorded test
values for mottled anorthosite specimen UCA7 are presented in Table 4-4 as an
example of the results obtained.
Effect of time on the tensile strength of several Bushveld Complex rock types
64
Table 4-4: Recorded UCS test values for specimen UCA7
MOTTLED ANORTHOSITE UG1 F/W DEPTH (1637.54-1643.27)m UCA7
Load, (kN)
Stress, (MPa)
Axial strain, εa x 10
-3
Radial
strain, εr x 10
-3
Volumetri
c strain, εv x 10
-3
Load, (kN)
Stress, (MPa)
Axial strain, εa x 10
-3
Radial
strain, εr x 10
-3
Volumetri
c strain, εv x 10
-3
0 0 0 0 0 115.247 111.359 1988 -481 1026
5.096 4.924 167 -6 155 120.735 116.662 2038 -519 1000
10.192 9.848 376 -13 350 125.047 120.829 2081 -545 991
15.288 14.772 527 -25 477 130.143 125.753 2131 -583 965
20.384 19.696 681 -38 605 135.239 130.677 2187 -615 957
25.088 24.242 811 -57 697 140.335 135.601 2230 -659 912
30.184 29.166 948 -82 784 145.431 140.525 2280 -697 886
35.672 34.469 1053 -101 851 150.526 145.448 2335 -748 839
40.376 39.014 1146 -120 906 155.622 150.372 2385 -798 789
45.08 43.559 1220 -139 942 160.326 154.918 2434 -855 724
50.175 48.482 1295 -158 979 165.03 159.463 2478 -906 666
55.271 53.407 1357 -184 989 170.126 164.387 2533 -982 569
60.367 58.331 1412 -203 1006 175.222 169.311 2577 -1064 449
65.071 62.876 1462 -222 1018 180.318 174.235 2633 -1191 251
70.167 67.800 1518 -247 1024 185.414 179.159 2682 -1343 -4
75.263 72.724 1573 -272 1029 190.118 183.705 2732 -1577 -422
80.359 77.648 1629 -298 1033 195.214 188.629 2800 -2300 -1800
85.063 82.194 1679 -317 1045 219 211.612 2800 -2300 -1800
90.159 87.118 1728 -342 1044
95.255 92.042 1784 -367 1050
100.351 96.966 1834 -393 1048 219kN load @ failure
105.055 101.511 1883 -424 1035
110.151 106.435 1939 -450 1039
The data from the test results was processed and used to plot stress-strain curves
as a visual aid, Figure 4-5. The average values of elastic properties of mottled
anorthosite (A) are indicated on the plot. The plot shows largely linear behaviour up
to the peak strength for the specimen, a trend largely repeated in the other four
specimens in the rock type test category (A), see Appendix B1.
Effect of time on the tensile strength of several Bushveld Complex rock types
65
Figure 4-5: Stress-Strain graph for mottled anorthosite specimen UCA7
4.3.2 Deformation properties
The specimens failed in a combined extension and shear fashion resulting in some
cases of conical shaped end pieces and a completely fractured or crushed middle
portion, Figure 4-6.
(a) (b)
Figure 4-6: Failure mode observed in specimen tested in uniaxial compression, (a) before the test and (b) after the test
Crack propagation parallel to the axis of the specimens was clearly visible in the
specimens tested indicating dilation in a direction perpendicular to the loading
0
20
40
60
80
100
120
140
160
180
200
-3000 -2000 -1000 0 1000 2000 3000 4000
Stre
ss (
MP
a)
millistrain
Stress-Strain UCA7
Stress-Axialstrain
Stress-Radialstrain
Volumetricstrain
Mottled Anorthosite-A Avg. (UCS ) = 174.51MPa Avg. Sec. E = 44.60GPa Avg. v = 0.20
Effect of time on the tensile strength of several Bushveld Complex rock types
66
direction. Dilation that occurred in the test specimens can be quantified through
volumetric strain analysis presented in the following section.
4.3.3 Analysis of volumetric strain
Based on Bieniawski (1967a)’s long term strength analysis, axial stress-volumetric
strain plots were used to evaluate the long term strength of the test specimens.
According to Bieniawski (1967a) the point of departure from linearity or the point of
inflexion of the stress-volumetric strain plot marks the “long term strength” of the
specimen. The rate of change of the stress-volumetric strain plot, as shown in Figure
4-7, was used to investigate the long term strength of the specimens as the inflexion
point was not clearly visible from the stress-strain plots.
Figure 4-7: Determination of the “long term strength” for specimen (UCA7)
Long term strengths were processed for each test category and average values
calculated. The significant variation shown in the test results can be attributed to
specimen inherent variability and defects and inconsistent strain gauge feedback.
Average long term strength values are presented here to investigate trends from the
nine test categories. The rate of volumetric strain-stress plots were expanded when
-40
-30
-20
-10
0
10
20
30
40
0 50 100 150 200
Ch
ange
in v
olu
me
tric
str
ain
(m
illis
trai
n)
Change in stress (MPa)
Long term strenghth UCA7
Rate of change of volumetricstrain
Long term strength = 90.2MPa = 0.59UCS
Effect of time on the tensile strength of several Bushveld Complex rock types
67
necessary to identify the long term strength value. For test specimen UCA7 the long
term strength was determined as 90.2MPa (~0.59 x UCS). A summary of the UCS
test results together with the long term strength values is given in the following
section (Table 4-5).
4.3.4 UCS test results summary
A summary of the average UCS test results is given in Table 4-5, and the detailed
set of test results is contained in Appendix B1. Further plots of representative
samples are presented in Appendix B. There do not appear to be any trends related
to the depth of placement of the rock specimens as the results showed a random
distribution along the length of the test core.
Table 4-5: Summaries of UCS test results (average values are presented here)
Rock type/ Code
M. A. (A)
S. A.N. (B)
P. (C)
M. A. (D)
N. (E)
S. A. N. (F)
A. N. (G)
S. A. (H)
M. A. (I)
Sample diameter, D (mm)
36.30 36.30 36.30 36.30 36.30 36.30 36.30 36.30 36.30
Sample length, L (mm)
80.74 84.79 81.66 81.13 83.71 82.87 80.99 81.03 80.98
L/D ratio 2.23 2.34 2.25 2.24 2.29 2.28 2.23 2.23 2.23
Sample mass, M (g)
231.41 254.20 270.30 230.93 261.32 248.10 253.48 237.80 232.32
Sample density, ρ (kg/m
3)
2769.46 2898.71 3198.41 2750.49 3016.40 2892.39 2990.22 2835.12 2772.17
Failure load, (kN)
180.60 139.40 129.80 140.50 96.00 154.60 114.00 159.60 182.20
UCS, σc (MPa)
174.51 134.70 125.42 135.76 92.76 149.38 110.15 154.22 176.05
Elastic Modulus, E (GPa)
44.60 33.32 35.49 39.01 30.90 40.65 37.90 42.64 45.31
Poisson’s ratio, v
0.20 0.21 0.17 0.28 0.19 0.21 0.15 0.22 0.19
Long term strength (MPa)
90.2 61.8 56.5 59.75 53.5 75.6 83.6 103.33 125.75
% of UCS 57 46 44 44 57 51.4 72.4 67 68.75
The average value of the “long term strength” for the nine categories of rock types
was 78MPa which is 56.39% of the UCS (0.56 x average UCS) value of the rock
types tested. The lowest “long term strength” values were recorded for pyroxenite
and mottled anorthosite rock types at 44% of their respective UCS values.
Effect of time on the tensile strength of several Bushveld Complex rock types
68
4.4 Brazilian Indirect Tensile (BIT) strength test
The (Multiple Testing System) MTS 815 servo-controlled machine was used to carry
out normal and time-dependent Brazilian Indirect Tensile (BIT) strength tests. The
MTS 815 rock testing machine together with its accessories is shown in Figure 4-8.
Figure 4-8: The MTS 815 rock testing machine used to load BIT discs
Curved platens (Figure 4-9) were used to ensure that tensile failure would initiate at
the centre of the BIT test discs (Hudson et al, 1972; Wang et al, 2004) and not at the
two contacts with the platens.
(a) (b)
Figure 4-9: Curved platens used in the BIT test set up, (a) before the test and (b) after the test
Effect of time on the tensile strength of several Bushveld Complex rock types
69
The spherical steel ball above the top platen helped align the applied stress through
the diameter of the rock disc specimens. The platens had a system of pegs and
guide holes to prevent non-uniform loading, as can be seen in Figure 4-9.
4.4.1 Normal Brazilian Indirect Tensile (BIT) strength test
A constant loading rate of 2kN/min was used to load specimens, targeted to fail in 3
to 4 minutes depending on their tensile strength. An example of a load-time plot, for
specimen NBA1, is shown in Figure 4-10.
Figure 4-10: Normal BIT load-time plot
The load drop trigger on the MTS machine was consistent with the initial appearance
of the tensile split of the Brazilian disc samples. The load at failure for each test
specimen was recorded and used to calculate the average tensile strength for the
different test categories. A summary of the results of the normal Brazilian tensile
strength tests is presented in Table 4-6 (elastic modulus values are those obtained
from the UCS tests).
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200 250 300
Load
(kN
)
Time (sec)
Load-Time NBA1
Load vs Time
Effect of time on the tensile strength of several Bushveld Complex rock types
70
Table 4-6: Summaries of Normal Brazilian Indirect Tensile BIT strength test results
Rock type Sample ID
Sample diameter, D (mm)
Sample thickness,
t (mm)
t/D ratio
Sample mass, M (g)
Average load at
failure, P (kN)
Average BIT
strength, σt (MPa)
Average Elastic
modulus, E (GPa)
Average strain at failure,
(millistrain)
Average Time-to-failure (sec)
Mottled Anorthosite
(A) DBA 36.30 19.27 0.53 54.26 8.19 7.46 46.72 0.16 220.71
Spotted Anorthositic Norite (B)
DBB 36.30 18.88 0.52 55.46 6.84 6.35 33.32 0.19 205.72
Pyroxenite (C)
DBC 36.30 18.97 0.52 62.67 7.43 6.89 35.40 0.19 206.77
Mottled Anorthosite
(D) DBD 36.30 18.77 0.52 53.84 6.83 6.38 39.01 0.16 138.02
Norite (E) DBE 36.30 18.36 0.51 57.67 6.92 6.62 30.90 0.21 160.35
Spotted Anorthositic Norite (F)
DBF 36.30 18.61 0.51 55.24 8.27 7.76 40.65 0.19 138.17
Anorthositic Norite (G)
DBG 36.30 17.65 0.49 56.31 7.71 7.65 37.90 0.20 203.85
Spotted Anorthosite
(H) DBH 36.30 17.59 0.48 51.29 7.11 7.10 42.64 0.17 213.83
Mottled Anorthosite
(I) DBI 36.30 17.06 0.47 48.93 6.82 7.04 45.31 0.16 214.03
A comparison between UCS and BIT strength values is presented in Table 4-7.
Table 4-7: Comparison of UCS and BIT strength test
Test category
BIT (MPa) UCS
(MPa) BIT/UCS UCS/BIT
A 7.91 174.51 0.05 22.05
B 6.61 134.7 0.05 20.38
C 7.18 125.42 0.06 17.47
D 6.60 135.76 0.05 20.57
E 6.69 92.76 0.07 13.87
F 7.99 149.38 0.05 18.69
G 7.45 110.15 0.07 14.79
H 6.87 154.22 0.04 22.45
I 6.59 176.05 0.04 26.71
Average 7.10 139.22 0.05 19.67
On average the BIT strength was found to be averagely 20 times lower than the UCS
of the same rock type. Typical strain values at failure were calculated based on the
elastic modulus for the rock type test category. The full set of the normal BIT test
results is contained in Appendix B3. Typical strain values at tensile failure ranged
1.6x10-1 to 2.1x10-1 millistrain, with an average value of 1.8 x 10-1 millistrain, well
within range of the magnitudes of the extension strain values determined, from the
Effect of time on the tensile strength of several Bushveld Complex rock types
71
numerical modelling, in the immediate walls of BC excavations, as reported in
Chapter 3.
4.4.1.1 Deformation characteristics
All valid test results had a clearly visible diametrical split observed in the direction of
loading, caused by induced tensile stress, as indicated by the samples of failed
discs, Figure 4-11.
Figure 4-11: Specimen failure in the BIT test
A few specimens, with suspected inherent defects, showed failure in more than one
place and in more than the diametrical direction, with a shorter time-to-failure and/or
smaller load at failure than expected. This was particularly observed in the
pyroxenite rock type, test category C. Some of the test specimens crushed where
they made contact with the top and bottom platens.
With the long term compressive strength and tensile characteristics of several BC
rock types established, including the typical extension strain at failure, it was
imperative to investigate the influence of time on the tensile strength of these rock
types.
Effect of time on the tensile strength of several Bushveld Complex rock types
72
4.4.2 Time-dependent Brazilian Indirect Tensile (BIT) strength test
Pre-determined load levels, derived from the tensile strength values recorded in the
normal BIT test results, were used in the time-dependent BIT strength tests. The
load levels were a percentage of those corresponding with the tensile strength
values for the respective rock test categories. Test sets, consisting of five specimens
per hold-load level for each test category, were conducted.
Constant hold-load level = X% of normal BIT load capacity
where X = 70; 75; 80; 85 and 90 representing 5% intervals.
Owing to limited availability of the MTS machine the longest time-dependent tests
were tested at 70% of tensile capacity, limiting the longest test runs to not more than
three days. The calculated load levels and corresponding expected strain values
based on the application of the elastic law are given in Table 4-8.
Table 4-8: Time-dependent BIT test loads
Rock type/ Specimen
I.D.
Mean load at failure, Pmean (kN)
Elastic Modulus, E (Gpa)
Static BIT test load, Phold = X% of Pmean (kN)
90% Phold, (kN)
(0.9 x ε) x 10
-3
85% Phold, (kN)
(0.85 x ε) x 10
-3
80% Phold, (kN)
(0.8 x ε) x 10
-3
75% Phold, (kN)
(0.75 x ε) x 10
-3
70% Phold, (kN)
(0.7 x ε) x 10
-3
SB%A 8.19 46.72 7.37 0.14 6.96 0.14 6.55 0.13 6.14 0.12 5.73 0.11
SB%B 6.84 33.32 6.16 0.17 5.81 0.16 5.47 0.15 5.13 0.14 4.79 0.13
SB%C 7.43 35.40 6.69 0.18 6.32 0.17 5.94 0.16 5.57 0.15 5.20 0.14
SB%D 6.83 39.01 6.15 0.15 5.81 0.14 5.46 0.13 5.12 0.12 4.78 0.11
SB%E 6.92 30.90 6.23 0.19 5.88 0.18 5.54 0.17 5.19 0.16 4.84 0.15
SB%F 8.27 40.65 7.44 0.17 7.03 0.16 6.62 0.15 6.20 0.14 5.79 0.13
SB%G 7.71 37.90 6.94 0.18 6.55 0.17 6.17 0.16 5.78 0.15 5.40 0.14
SB%H 7.11 42.64 6.40 0.15 6.04 0.14 5.69 0.13 5.33 0.12 4.98 0.12
SB%I 6.82 45.31 6.14 0.14 5.80 0.13 5.46 0.12 5.12 0.12 4.77 0.11
A theoretical stress-strain plot at the various load levels for the various rock types
test categories is shown in Figure 4-12. Included in the plot is the strain sustained in
a specimen at tensile failure shown at the peak of each individual plot. This graph
depicts typical strains calculated at different load levels under indirect or induced
tension.
Effect of time on the tensile strength of several Bushveld Complex rock types
73
Figure 4-12: Calculated strains at various load levels for the nine test categories
Loads on each test specimen were increased at a rate of 2kN/min up to a constant
load corresponding to the required percentage of the load capacity. The time-to-
failure, T(s), the time from the onset of the constant load stage up to test specimen
failure, was recorded for complete test runs where specimen failure was observed.
Some of the test runs, particularly ones at 90% of tensile load, failed during the load
application stage, before reaching the constant load phase. Other test runs with
similar premature failure results were attributed to variability and inherent defects in
the test specimens, resulting in rapid failure and lower strength. An example of this is
given for sample SB90A1, whose constant time-dependent test load would have
been 7.33kN but failure occurred on reaching 7.3kN during the loading stage, Figure
4-13.
A
A
B
B
C
C
D
D
E
E
F
F
G H
H
I
I
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6 7 8 9
mill
istr
ain
Load (kN)
Load-Strain
A
B
C
D
E
F
G
H
I
Effect of time on the tensile strength of several Bushveld Complex rock types
74
Figure 4-13: Time-dependent Load-Time plot
The variation in t/D ratio for the test specimens was so negligible that specimen
shape and size was ruled out as influencing the strength of the samples. A load-time
plot where the specimen loaded at constant load until the specimen failed in tension
is presented in Figure 4-14.
Figure 4-14: Time-dependent BIT Load-Time plot
0
1
2
3
4
5
6
7
8
0 50 100 150 200 250
Load
(kN
)
Time (sec)
Load-Time SB90A1
Load vs time SB90A1
0
1
2
3
4
5
6
7
0 10000 20000 30000 40000
Load
(kN
)
Time (sec)
Load-Time SB80A3
Load vs time SB80A3
Effect of time on the tensile strength of several Bushveld Complex rock types
75
In a few test runs, particularly in the low load tests at 70%, failure did not occur within
three days, and in other cases the MTS machine tripped due to overheating. In
cases in which times to failure were expected to be longer, tests at those particular
load levels were aimed to run over weekends in an attempt to achieve valid times-to-
failure. Valid test results were therefore only recorded if the initial loading build-up
was completed to the hold stage, if the MTS machine did not trigger the stop
command due to external vibrations or overheating, and if the test was completed
within three days.
4.4.3 Time-dependent BIT test results
Each set of test specimens tested in this research used a single constant load. The
time-dependent test results for the nine specimen categories are summarised in
Table 4-9.
Table 4-9: Time-dependent test results
Rock type/
Specimen I.D.
Mean BIT
strength, Pmean (kN)
Static BIT test load, X% of Pmean (kN) and Time-to-failure, T (s)
90% Time, T
(s) 85%
Time, T (s)
80% Time, T
(s) 75%
Time, T (s)
70% Time, T
(s)
SB%A 8.19 7.37 268 6.96 972 6.55 11658 6.14 39831 5.73 111480
SB%B 6.84 6.16 1587 5.81 2200 5.47 4578 5.13 19837 4.79 62226
SB%C 7.43 6.69 16830 6.32 38695 5.94 33705 5.57 207423 5.20 23605
SB%D 6.83 6.15 229 5.81 16328 5.46 82700 5.12 36306 4.78 151889
SB%E 6.92 6.23 1652 5.88 375 5.54 10327 5.19 1679 4.84 60706
SB%F 8.27 7.44 - 7.03 375 6.62 1705 6.20 2698 5.79 60709
SB%G 7.71 6.94 643 6.55 147 6.17 - 5.78 2483 5.40 805
SB%H 7.11 6.40 4214 6.04 12291 5.69 8168 5.33 67109 4.98 62350
SB%I 6.82 6.14 6213 5.80 45191 5.46 33038 5.12 38993 4.77 39151
The individual creep test results show a random scatter in the time-to-failure, and
hence it was decided to use a logarithmic trend line to investigate the time-
dependent trends. The trend line of the time-to-failure starts off with a steep gradient
which flattens, with time, to a strength value below which specimen failure may not
be expected over an infinite period of time. This value may be taken as the long term
tensile strength of the rock type. The limitation in determining the long term tensile
strength of BC rocks in this way is the limited range of test loads and the limited
number of creep tests available to define a smooth curve of load vs time-to-failure.
Effect of time on the tensile strength of several Bushveld Complex rock types
76
Ideally creep test loads at intervals ranging up to 90% of the tensile strength should
be used to investigate time-dependent trends of the rock types. In addition, large
numbers of tests would be required to take the rock variability satisfactorily into
account. The results for test category B shown in Figure 4-15 illustrate the scatter in
the results and the trend in the time-dependent results.
Figure 4-15: Time-to-failure plot for test category B (Rock type: spotted anorthositic norite)
In test category B, minimum creep loads of 60% of the normal tensile strength were
applied, while the other eight test categories the minimum was 70% of tensile
strength. A theory that the long term tensile strength of a rock type is expected to be
lower than its compressive long term strength established via UCS tests is mooted
here. Plots of load against average time-to-failure for all nine test categories are
presented in Figures 4-16 and Figure 4-17. A full set of the time-dependent results
and plots for the nine test categories is presented in Appendix B3.
% Tensile Strength = -5.018ln(Time) + 124.59 R² = 0.8008
0
10
20
30
40
50
60
70
80
90
100
0 20000 40000 60000 80000 100000
% o
f te
nsi
le s
tre
ngt
h
Time-to-failure (s)
% tensile strength-Time (B)
Average time-to-failure
Test set 1
Test set 2
Test set 3
Test set 4
Test set 5
Test set 6
Logarithmic trend line
Effect of time on the tensile strength of several Bushveld Complex rock types
77
Figure 4-16: Load-Time plot for averages of all the test results
Figure 4-17: Percentage load-Time plot for averages of all test results
Extension strains were calculated from the tensile strength test results, making use
of the elastic moduli. From these data a plot of strain-time is shown in Figure 4-18,
0
1
2
3
4
5
6
7
0 10000 20000 30000 40000 50000 60000
Load
(kN
)
Time (sec)
Tensile load-Average time
Average time-to-failure
0
10
20
30
40
50
60
70
80
90
100
0 10000 20000 30000 40000 50000 60000
% o
f te
nsi
le s
tre
ngt
h
Time (sec)
% tensile strength-Average time
Average time-to-failure
Effect of time on the tensile strength of several Bushveld Complex rock types
78
giving an indication of times for rock to attain strains at which extension strain failure
may occur according to the analyses presented in Chapter 3.
Figure 4-18: Strain-Time plot for averages of all test results
The main limitation of the test load ranges applied in these creep tests is that the
time-to-failure results were influenced by test machine availability, and test loads
lower than at least 50% should ideally have been used. However, the results provide
some data when none existed before, and are conclusive in showing the time-
dependency of the tensile strength of several BC rock types.
4.5 Conclusions
Elastic properties of several BC rock types, and their interpreted long term
compressive strengths, were established through the UCS test. Tensile properties
for these rock types were established under normal and time-dependent indirect
tension. The following points were highlighted:
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 10000 20000 30000 40000 50000 60000
mill
istr
ain
Time (sec)
Strain-Average time-to-failure
Average time-to-failure
Effect of time on the tensile strength of several Bushveld Complex rock types
79
The average “long term strength” of the rock types calculated from the UCS
tests was 78 MPa which is equivalent to 56.5% of the average UCS for the
rock types.
Tensile strengths (σt) of BC rock types were on average 5% of the
corresponding UCS strength (σc).
Using the elastic properties of the BC rock types and Hooke’s constitutive
laws of elasticity in rock, typical extension strain values at tensile failure were
calculated giving maximum and minimum average strain values of 1.8 x 10-4
and 1.2 x 10-4 respectively.
Generally the tensile strength of the BC rocks showed time-dependency
although individual results showed a lot of variance in the time to failure.
The time for the time-dependent tests was limited by machine availability to
not more than three days, thus preventing the investigation of a full range of
creep test loads (0 – 90% of the tensile strength).
The average time-to-failure plots showed increasing creep failure time with
decreasing creep load. However, owing to the limited creep test periods, the
ultimate long term tensile strength, if it existed, could not be concluded from
the research. Nevertheless, the results showed that the long term tensile
strength is less than 70% of the normal tensile strength.
Effect of time on the tensile strength of several Bushveld Complex rock types
80
CHAPTER 5
DISCUSSION OF STRESS-STRAIN ANALYSIS RESULTS
5.1 Introduction
Evaluation of the stress and strain distributions in the Bushveld Complex (BC) mining
environment was conducted using numerical analyses, and laboratory strength
testing was used to evaluate the strength characteristics of BC rock types. Chapter 3
presented the results of numerical analyses of the distribution of stress and strain
around modelled excavations in BC rock masses. Laboratory rock strength test
results were reported in Chapter 4, including a comprehensive characterisation of
the deformational behaviour of several BC rock types loaded in compression and
indirect tension. The current chapter correlates findings from numerical analyses with
laboratory rock strength test results to establish the implications of the effect of time
on the stability of mining excavations in the BC.
5.2 Results of laboratory testing
From the compressive and tensile strength tests carried out, the following key
outputs may be summarised:
1. Average UCS values obtained for the BC rocks varied between 93MPa and
176MPa, with an average value of 138MPa.
2. The average long term strength of the rocks, interpreted from the volumetric
strain curves in the UCS tests, was 78MPa, which is 56% of the UCS. The
lowest long term strength value obtained was 44% of the corresponding UCS
value.
3. Tensile strength magnitudes of the rocks were found to be between 4% and
7% of the UCS magnitudes (the tensile strength magnitude is about 20 times
lower than the UCS magnitude).
4. The minimum long term tensile strengths of the rocks could not be determined
owing to testing machine availability, but are certainly less than 70% of their
normal tensile strengths.
Effect of time on the tensile strength of several Bushveld Complex rock types
81
5. Extension strain magnitudes at strength failure interpreted from the normal
tensile strength tests indicate a range of between 1.6 x 10-4 and 2.1 x 10-4.
Values corresponding with the long term tensile strength would therefore be
less than 70% of this range, or less than 1.1 x 10-4 to 1.5 x 10-4.
5.3 Results of the numerical analyses
The following points stand out from the numerical analyses of stress-strain
distribution:
1. Numerical models gave higher ranges of stress (25 to 37 MPa) in the pillar
core than in the outer walls consisting of the immediate stope hanging walls
and sidewalls with stresses of 5 to 15MPa.
2. The models illustrated that the outer wall rock of mine excavations may well
have low compressive and in some instances tensile conditions.
3. The stress conditions expected in the excavation walls of the models are
lower than the UCS, but are within range of the tensile strengths of the rock
types investigated in this research.
4. The magnitudes of extension strains determined from the modelling (Figure 5-
1) are as large as 1.05 x 10-3, well exceeding the extension strain magnitudes
at tensile failure obtained from laboratory indirect tensile strength test results,
summarized in Section 5.2 above.
Note that observations made in actual BC mine excavations revealed that fracturing
of intact rock occurs over a protracted time period; possibly due to the extension of
fractures, and that the manifestation of such fracturing was curbed by installed
support.
Effect of time on the tensile strength of several Bushveld Complex rock types
82
Figure 5-1: Distribution of extension strain around an in-stope pillar
Figures 5-2 and 5-3 illustrate the theoretical magnitudes of the extent of the influence
of critical extension strain at which fracture propagation is anticipated. These
magnitudes may be modified and reduced by the presence of parting planes and
other weakness planes in the rock mass. The main purpose of the analyses was to
demonstrate the potential occurrence of large zones of extension in underground
excavations in the BC mines.
Effect of time on the tensile strength of several Bushveld Complex rock types
83
Figure 5-2: Illustration of the zone in a stope sidewall prone to fracture propagation
Figure 5-3: Illustration of zones in the stope hanging wall prone to fracture propagation
Effect of time on the tensile strength of several Bushveld Complex rock types
84
5.3 Implications from the numerical analyses and the laboratory testing
At the surface of excavations walls, rock is subjected to low confinement normal to
the surface, whilst subjected to high compressive stresses in the plane of the
surface. Under such conditions fractures may develop due possibly to the induced
tensile stress and extension strain sustained in the excavation wall rock. The walls
of most Bushveld Complex mine excavations are exposed to these conditions for
periods of time varying from months to years. The research has shown that these
excavations may be susceptible to stress induced fracturing under such conditions,
particularly when time-dependency is taken into account.
Images of zones around modelled excavation walls prone to fracture propagation,
according to this discussion are depicted in Figures 5-2 to 5-3. Note that only
extension strain values (negative strains) were contoured in both images. In these
illustrations, the estimated depth of extension strain, representative of the magnitude
of extension strain at tensile failure, is read off as 0.5m into the pillar sidewall and
18.7m into the stope hanging wall. However these values are theoretical and do not
consider the presence of parting planes and other weakness planes which may
modify the magnitudes of the zones depicted here.
The research results have thus helped to explain some of the observed failure in
intact rock forming the rock mass hosting mines in the BC.
Effect of time on the tensile strength of several Bushveld Complex rock types
85
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
The research detailed in this dissertation has dealt with the investigation of stress
and strain conditions influencing spalling of wall rock in Bushveld Complex mine
excavations. This involved a review of the Bushveld Complex mining environment, a
review of literature relevant to time-dependent behaviour of rock, laboratory testing
of Bushveld Complex rocks in uniaxial compression and in indirect tension, including
time-dependent indirect tension, and elastic numerical modelling of typical mine
excavations. The following are the conclusions from the research:
There have been very few time-dependent or creep tests carried out in South
Africa on rock, particularly on Bushveld Complex rock types. The laboratory
testing carried out for the research described in this dissertation has now
provided some data in this regard, which represents a contribution of new
knowledge.
The Brazilian test does not appear to have been used before in time-
dependent tests, and the new data provided from this research again
represent a contribution of new knowledge. The BIT creep tests proved to be
quick and effective for establishing time-dependent behaviour of rock under
(indirect) tension.
The magnitude of the tensile strength of BC rock types was equal to
approximately 5% of their compressive strength magnitudes.
The long term uniaxial compressive strength of the BC rocks, interpreted from
the axial stress-volumetric strain graph from the UCS test, is, on average,
78MPa, 56% of the UCS value.
The tensile strength of the BC rock types was found to be time-dependent.
However, the minimum long term tensile strength value could not be
determined in this research owing to limited testing machine availability.
Although the logarithmic time-to-failure of the nine test categories in the
research showed a general time-dependent trend, the individual test
specimen failure times showed a large variation.
Effect of time on the tensile strength of several Bushveld Complex rock types
86
Extension strains at tensile strength failure ranged between 1.6 x 10-4 and 2.1
x 10-4. Values corresponding with the long term tensile strength are less than
70% of this range, namely, less than 1.1 x 10-4 to 1.5 x 10-4.
Numerical analysis of BC excavations was carried out using elastic models
and assuming homogeneity of material based on average elastic properties of
several BC rock types. The compressive stresses determined in the models
were found to be an order of magnitude lower than the compressive strength
of the rock. Tensile stresses were of comparable magnitude to the tensile
strength of the BC rock types investigated in this research.
The numerical models showed that large zones of extension strain can occur
around BC excavations, and that the magnitudes of the extension strain
exceed the critical values determined from the laboratory testing.
Observations made in actual BC mine excavations revealed that fracturing of
intact rock occurs over a protracted time period, and that its manifestation is
curbed by installed support.
There is no conclusive prerequisite for tensile conditions to exist, to induce
critical extension strain. Both compressive and tensile stress conditions were
observed to generate critical (negative) extension strain.
The research that has been described has focused on the tensile and extension
behaviour of Bushveld Complex rocks. This research could not conclusively
establish the long term tensile strengths, but managed to establish the time-
dependent behaviour of several BC rock types. What has been established is that
the long term tensile strength is less than 70% of the normal tensile strength, and
probably less than 60% of this value. Numerical modelling has established that
substantial zones of extension strain occur around BC mining excavations, and that
the magnitudes of these strains exceed the strain magnitudes corresponding with
tensile strength failure. The implication of this is that there are substantial zones
surrounding BC mine excavations that will be prone to spalling conditions and
perhaps more significant failure.
The main conclusion from the research is that tensile and extension behaviour is
very important and should be given more attention. It is recommended that further
Effect of time on the tensile strength of several Bushveld Complex rock types
87
programmes of time-dependent testing of BC rocks should be carried out in the
future.
Effect of time on the tensile strength of several Bushveld Complex rock types
88
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Effect of time on the tensile strength of several Bushveld Complex rock types
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APPENDICES
Appendix A: Geological log sheet for drill hole BH6082
Borehole BH6082 was used to prepare laboratory test specimens in this research
and the log sheet is given in Table A1-1. The drill hole was part of Impala Platinum’s
Rustenburg surface exploration drilling in the Rustenburg Layered Suite. The
markings on the log sheet were made during the preparation of samples.
Appendix A1-1: Geological log sheet for borehole BH6082
Effect of time on the tensile strength of several Bushveld Complex rock types
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Effect of time on the tensile strength of several Bushveld Complex rock types
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Effect of time on the tensile strength of several Bushveld Complex rock types
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Effect of time on the tensile strength of several Bushveld Complex rock types
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Effect of time on the tensile strength of several Bushveld Complex rock types
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Effect of time on the tensile strength of several Bushveld Complex rock types
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Effect of time on the tensile strength of several Bushveld Complex rock types
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Appendix B: Laboratory rock strength test results
B1 UCS test results and long term strength analysis
Uniaxial compressive strength UCS results were presented briefly in Chapter 4. For
space and organisation of the thesis the full set of results and graph plots of the nine
test categories are given in this section to give a full picture of the UCS test results,
Table B1-1.
Table B1-1: Uniaxial compressive strength test results
Rock type/ Code
Sample ID
Sample diameter, D (mm)
Sample length, L (mm)
L/D ratio
Sample mass, M (g)
Sample density, ρ (kg/m
3)
Failure load (kN)
UCS, σc (MPa)
Elastic Modulus, E (GPa)
Poisson’s ratio, ѵ
Long term strength, L-T, (MPa)
(LT/UCS) %
Mottled Anorthosite A
UCA6 30.30 82.35 2.27 234.40 2750.00 159.00 153.67 42.34 0.10 111.00 72 UCA7 36.30 83.60 2.30 233.40 2755.50 219.00 211.61 54.89 0.23 91.00 72 UCA8 36.30 83.65 2.30 237.40 2750.37 184.00 177.79 44.36 0.11 111.00 63 UCA9 36.30 82.50 2.27 234.30 2746.54 181.00 174.89 49.00 0.30 51.00 29
UCA10 36.30 83.35 2.30 237.80 2741.07 178.00 172.00 43.00 0.19 87.00 51
Average 36.30 83.09 2.29 235.46 2748.70 184.20 177.99 46.72 0.19 90.20 57
Spotted Anorthositic Norite B
UCB6 36.30 84.80 2.34 253.70 2890.82 142.00 137.21 33.47 0.23 60.00 43 UCB7 36.30 84.60 2.33 255.00 2912.57 142.00 137.21 34.31 0.20 77.00 56 UCB8 36.30 84.85 2.34 254.20 2903.92 141.00 136.24 32.67 0.22 60.00 44 UCB9 36.30 85.00 2.34 253.50 2881.75 135.00 130.45 30.94 0.18 58.00 44
UCB10 36.30 84.70 2.33 254.60 2904.50 137.00 132.38 35.20 0.20 54.00 41
Average 36.30 84.79 2.34 254.20 2898.71 139.40 134.70 33.32 0.21 61.80 46
Pyroxenite C UCC6 36.30 81.80 2.25 271.90 3211.83 103.00 99.53 33.72 0.01 - - UCC7 36.30 81.40 2.24 268.60 3188.44 178.00 172.00 39.17 0.42 54.00 32 UCC8 36.30 81.70 2.25 271.40 3209.85 108.00 104.36 32.29 0.18 49.00 47 UCC9 36.30 82.00 2.26 269.70 3178.07 129.00 124.65 36.32 0.11 64.00 51
UCC10 36.30 81.40 2.24 269.90 3203.87 131.00 126.58 35.95 0.14 59.00 46
Average 36.30 81.66 2.25 270.30 3198.41 129.80 125.42 35.49 0.17 56.50 44
Mottled Anorthosite D
UCD6 36.30 81.30 2.23 233.00 2769.25 145.00 140.11 38.54 0.48 43.00 31 UCD7 36.30 81.20 2.24 231.70 2757.19 139.00 134.31 - - - - UCD8 36.30 81.30 2.24 232.50 2763.31 140.00 135.28 36.73 0.14 103.00 76 UCD9 36.30 81.00 2.23 230.70 2752.07 140.00 135.28 42.70 0.41 44.00 32
UCD10 36.30 81.00 2.23 228.80 2729.40 143.00 138.18 37.61 0.30 46.00 34
Average 36.30 81.13 2.24 230.93 2750.49 140.50 135.76 39.01 0.28 59.75 44
Norite E UCE6 36.30 83.35 2.23 260.30 3017.63 90.00 86.96 30.31 0.17 64.00 74 UCE7 36.30 84.00 2.31 266.00 3059.84 104.00 100.49 32.60 0.24 46.50 46 UCE8 36.30 83.60 2.30 260.20 3007.45 100.00 96.63 30.10 0.16 53.00 55 UCE9 36.30 83.80 2.31 259.10 2987.59 97.00 93.73 31.26 0.20 49.00 51
UCE10 36.30 83.80 2.31 261.00 3009.49 89.00 86.00 30.25 0.18 55.00 57
Average 36.30 83.71 2.29 261.32 3016.40 96.00 92.76 30.90 0.19 53.50 57
Spotted Anorthositic Norite F
UCF6 36.30 84.00 2.31 250.50 2881.54 161.00 155.57 40.44 0.18 80.00 51 UCF7 36.30 83.70 2.31 250.20 2888.41 152.00 146.87 40.35 0.21 77.00 52 UCF8 36.30 83.85 2.31 253.90 2925.88 161.00 155.57 40.98 0.23 77.00 49 UCF9 36.30 83.80 2.31 252.70 2913.79 142.00 137.21 40.24 0.20 67.00 49
UCF10 36.30 79.00 2.18 233.20 2852.32 157.00 151.70 41.25 0.23 71.00 56
Average 36.30 82.87 2.28 248.10 2892.39 154.60 149.38 40.65 0.21 75.60 51.4
Anorthositic Norite G
UCG6 36.30 82.15 2.26 256.40 3015.83 93.00 89.86 34.14 0.13 81.00 76 UCG7 36.30 82.00 2.26 260.80 3073.20 120.00 115.95 47.58 0.17 80.00 69 UCG8 36.30 80.50 2.22 242.70 2913.20 126.00 121.75 32.52 0.14 105.00 86 UCG9 36.30 79.80 2.20 239..5 2900.01 114.00 110.15 40.87 0.16 81.00 70
UCG10 36.30 80.50 2.22 254.00 3048.84 117.00 113.05 34.40 0.15 71.00 61
Average 36.30 80.99 2.23 253.48 2990.22 114.00 110.15 37.90 0.15 83.60 72.4
Spotted Anorthosite H
UCH6 36.30 79.10 2.18 231.10 2823.06 159.00 153.64 40.70 0.16 118.00 77 UCH7 36.30 80.90 2.23 235.80 2816.39 181.00 174.89 48.53 0.22 90.00 51 UCH8 36.30 82.40 2.27 239.80 2812.02 145.00 140.11 39.27 0.31 - - UCH9 36.30 79.55 2.19 230.50 2799.80 162.00 156.54 42.16 0.22 - -
UCH10 36.30 83.20 2.29 251.80 2924.35 151.00 145.91 42.54 0.17 102.00 73
Average 36.30 81.03 2.23 237.80 2835.12 159.60 154.22 42.64 0.22 103.33 67
Mottled Anorthosite I
UCI6 36.30 79.80 2.20 229.20 2775.29 196.00 189.39 49.22 0.19 139.00 74 UCI7 36.30 81.80 2.25 235.30 2779.49 197.00 190.35 44.51 0.18 155.00 82 UCI8 36.30 79.00 2.18 227.10 2777.71 156.00 150.74 42.88 0.17 - - UCI9 36.30 83.80 2.31 239.50 2761.59 183.00 176.83 46.06 0.22 101.00 57
UCI10 36.30 80.50 2.22 230.50 2766.76 179.00 172.96 43.89 0.21 108.00 62
Average 36.30 80.98 2.23 232.32 2772.17 182.20 176.05 45.31 0.19 125.75 68.8
Representative stress-strain plots from the UCS are given in Figures B1-1 to B1-8.
Effect of time on the tensile strength of several Bushveld Complex rock types
108
Figure B1-1: Stress-strain graph for spotted anorthositic norite (S.A.N.) rock type specimen UCB6
Figure B1-2: Stress-strain graph for pyroxenite (P.) rock type specimen UCC8
0
20
40
60
80
100
120
140
-3000 -2000 -1000 0 1000 2000 3000 4000
stre
ss (
MP
a)
millistrain
Stress-Strain UCB6
Stress-Axial strain
Stress-Radial strain
Volumetric strain
Spotted Anorthositic Norite-B Avg. (UCS ) = 134.70MPa Avg. Sec. E = 33.32GPa Avg. v = 0.21
0
10
20
30
40
50
60
70
80
90
-2000 -1000 0 1000 2000 3000
Ste
ss (
MP
a)
millistrain
Stress-Strain UCC8
Stress-Axial strain
Stress-Radial strain
Volumetric strain
Pyroxenite-C Avg. (UCS ) = 125.42MPa Avg. Sec. E = 35.49GPa Avg. v = 0.17
Effect of time on the tensile strength of several Bushveld Complex rock types
109
Figure B1-3: Stress-strain graph for mottled anorthosite (M.A.) rock type specimen UCD10
Figure B1-4: Stress-strain graph for norite (N.) rock type specimen UCE7
0
20
40
60
80
100
120
140
-4000 -3000 -2000 -1000 0 1000 2000 3000 4000
Stre
ss (
MP
a)
millistrain
Stress-Strain UCD10
Stress-Axial strain
Stress-Radial strain
Volumteric strain
Mottled Anorthosite-D Avg. (UCS ) = 135.76MPa Avg. Sec. E = 39.01GPa Avg. v = 0.28
0
10
20
30
40
50
60
70
80
90
-2000 -1000 0 1000 2000 3000
Stre
ss (
MP
a)
millistrain
Stress-Strain UCE7
Stress-Axial strain
Stress-Radial strain
Volumetric strain
Norite-E Avg. (UCS ) = 92.76MPa Avg. Sec. E = 30.90GPa Avg. v = 0.19
Effect of time on the tensile strength of several Bushveld Complex rock types
110
Figure B1-5: Stress-strain graph for spotted anorthositic norite (S.A.N.) rock type specimen UCF6
Figure B1-6: Stress-strain graph for anorthositic norite (A.N.) rock type specimen UCG7
0
20
40
60
80
100
120
140
160
-2000 -1000 0 1000 2000 3000 4000
Stre
ss (
MP
a)
millistrain
Stress-Strain UCF6
Stress-Axial strain
Stress-Radial strain
Volumetric strain
Spotted Anorthositic Norite-F Avg. (UCS ) = 149.38MPa Avg. Sec. E = 40.65GPa Avg. v = 0.21
0
20
40
60
80
100
120
-1500 -1000 -500 0 500 1000 1500 2000 2500
Stre
ss (
MP
a)
millistrain
Stress-Strain UCG7
Stress-Axial strain
Stress-Radial strain
Volumetric strain
Anorthositic Norite-G Avg. (UCS ) = 110.15MPa Avg. Sec. E = 37.90GPa Avg. v = 0.15
Effect of time on the tensile strength of several Bushveld Complex rock types
111
Figure B1-7: Stress-strain graph for spotted anorthosite (S.A.) rock type specimen UCH7
Figure B1-8: Stress-strain graph for mottled anorthosite (M.A.) rock type specimen UCI9
0
20
40
60
80
100
120
140
160
180
-2000 -1000 0 1000 2000 3000
Stre
ss (
MP
a)
millistrain
Stress-Strain UCH7
Stress-Axial strain
Stress-Radial strain
Volumetric strain
Spotted Anorthosite-H Avg. (UCS ) = 154.22MPa Avg. Sec. E = 42.64GPa Avg. v = 0.22
0
20
40
60
80
100
120
140
160
180
-5000 -3000 -1000 1000 3000 5000
Stre
ss (
MP
a)
millistrain
Stress-Strain UCI9
Stress-Axial strain
Stress-Radial strain
Volumetric strain
Spotted Anorthositic Norite-B Avg. (UCS ) = 176.05MPa Avg. Sec. E = 54.31GPa Avg. v = 0.19
Effect of time on the tensile strength of several Bushveld Complex rock types
112
To assess the long term strength of the various BC rock types volumetric strain-
stress plots were used following the analysis by Bieniawski (1967) discussed in
Chapter 2 and illustrated in section 4-3-3. The point of inflection could not be read off
easily from a casual inspection of the stress-strain plots shown in Figures B1-1 to
B1-8 so the rate of change of volumetric strain with stress was used to determine the
point where the plot crossed the horizontal stress axis. The determination of the long
term strength is illustrated in Figures B1-9 to B1-16 through representative plots. A
summary of the average values obtained here was presented in the UCS test results
in Chapter 4 and in Table B1-1.
Figure B1-9: Rate of change of volumetric strain with respect to stress (UCB6)
-100
-80
-60
-40
-20
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Ch
ange
in v
olu
me
tric
str
ain
(m
illis
trai
n)
Stress (MPa)
Long Term Strength UCB6
Volumetric strain
Spotted Anorthositic Norite-B Avg. Long-term (L-T) strength = 61.8MPa L-T/Avg. UCS = 46%
Effect of time on the tensile strength of several Bushveld Complex rock types
113
Figure B1-10: Rate of change of volumetric strain with respect to stress (UCC8)
Figure B1-11: Rate of change of volumetric strain with respect to stress (UCD10)
-250
-200
-150
-100
-50
0
50
100
0 20 40 60 80 100
Ch
ange
in v
olu
me
tric
str
ain
(m
illis
trai
n)
Stress (MPa)
Long Term Strength UCC8
Volumetric strain
Pyroxenite-C Avg. Long-term (L-T) strength = 56.5MPa L-T/Avg. UCS = 44%
-200
-150
-100
-50
0
50
100
0 20 40 60 80 100 120 140
Ch
ange
in v
olu
me
tric
str
ain
(m
illis
trai
n)
Stress (MPa)
Long Term Strength UCD10
Volumetric strain
Mottled Anorthosite-D Avg. Long-term (L-T) strength = 59.75MPa L-T/Avg. UCS = 44%
Effect of time on the tensile strength of several Bushveld Complex rock types
114
Figure B1-12: Rate of change of volumetric strain with respect to stress (UCE7)
Figure B1-13: Rate of change of volumetric strain with respect to stress (UCF6)
-200
-150
-100
-50
0
50
0 20 40 60 80 100
Ch
ange
in v
olu
me
tric
str
ain
(mill
istr
ain
)
Stress (MPa)
Long Term Strength UCE7
Volumetric strain
Norite-E Avg. Long-term (L-T) strength = 53.5MPa L-T/Avg. UCS = 57%
-160
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
0 20 40 60 80 100 120 140 160
Ch
ange
in v
olu
me
tric
str
ain
(m
illis
trai
n)
Stress (MPa)
Long Term Strength UCF6
Volumetric strain
Spotted Anorthositic Norite-F Avg. Long-term (L-T) strength = 75.6MPa L-T/Avg. UCS = 51.4%
Effect of time on the tensile strength of several Bushveld Complex rock types
115
Figure B1-14: Rate of change of volumetric strain with respect to stress (UCG7)
Figure B1-15: Rate of change of volumetric strain with respect to stress (UCH10)
-120
-100
-80
-60
-40
-20
0
20
40
0 20 40 60 80 100 120
Ch
ange
in v
olu
me
tric
str
ain
(m
illis
trai
n
Stress (MPa)
Long term Strength UCG7
volumetric strain
Anorthositic Norite-G Avg. Long-term (L-T) strength = 83.6MPa L-T/Avg. UCS = 72.4%
-20
-10
0
10
20
30
40
0 20 40 60 80 100 120 140 160
Long Term Strength UCH10
Series1
Spotted Anorthosite-H Avg. Long-term (L-T) strength = 103.33MPa L-T/Avg. UCS = 67%
Effect of time on the tensile strength of several Bushveld Complex rock types
116
B1-16: Rate of change of volumetric strain with respect to stress (UCI9)
Due to the noise in the data plots after the peak strength, the first intercept on the
stress (horizontal) axis was recorded as the “long term strength” for the particular
specimen.
-5
0
5
10
15
20
25
30
35
40
0 50 100 150 200
Ch
ange
in v
olu
me
tric
str
ain
(m
illis
trai
n)
Stress (MPa)
Long Term Strength UCI9
Volumetric strain
Mottled Anorthosite-I Avg. Long-term (L-T) strength = 101.75MPa L-T/Avg. UCS = 57.5%
Effect of time on the tensile strength of several Bushveld Complex rock types
117
B2 Normal Brazilian Indirect Tensile (BIT) strength test results
The full set of the normal BIT test results for all nine test categories is given in Table
B2-1.
Table B2-2: Normal Brazilian Indirect Tensile (BIT) strength test results
Rock type Sample ID Sample diameter, D
(mm)
Sample thickness, t
(mm)
t/D ratio Sample mass, M (g)
Load at failure, P
(kN)
BIT, σt (MPa) Time-to-failure (s)
Mottled Anorthosite A
DBA1 36.30 18.80 0.52 53.20 7.90 7.37 286.28 DBA2 36.30 19.15 0.53 54.10 8.74 8.00 241.70 DBA3 36.30 19.70 0.54 54.60 6.95 6.19 230.18 DBA4 36.30 19.40 0.53 54.70 8.29 7.49 161.52 DBA5 36.30 19.30 0.53 54.70 9.08 8.25 183.86
Average 36.30 19.27 0.53 54.26 8.19 7.46 220.71
Spotted Anorthositic
Norite B
DBB1 36.30 18.20 0.50 51.90 7.10 6.84 265.70 DBB2 36.30 18.00 0.50 52.00 5.95 5.80 207.68 DBB3 36.30 19.00 0.52 56.10 6.31 5.82 176.91 DBB4 36.30 19.00 0.54 57.90 7.63 6.86 180.41 DBB5 36.30 19.50 0.54 57.00 7.07 6.36 181.27 DBB6 36.30 19.00 0.52 56.70 6.90 6.37 191.20 DBB7 36.30 18.75 0.52 55.70 6.78 6.34 196.58 DBB8 36.30 19.10 0.53 56.40 7.00 6.43 246.00
Average 36.30 18.88 0.52 55.46 6.84 6.35 205.72
Pyroxenite C DBC1 36.30 19.50 0.54 64.20 5.55 4.99 217.16 DBC2 36.30 18.20 0.50 60.20 7.05 6.79 267.60 DBC3 36.30 19.20 0.53 63.10 6.60 6.03 200.49 DBC4 36.30 18.40 0.51 60.00 9.98 9.51 186.15 DBC5 36.30 19.20 0.53 63.40 6.87 6.28 192.86 DBC6 36.30 19.10 0.53 63.20 8.19 7.52 180.15 DBC7 36.30 19.20 0.53 64.60 7.79 7.12 203.01
Average 36.30 18.97 0.52 62.67 7.43 6.89 206.77
Mottled Anorthosite D
DBD1 36.30 18.80 0.52 54.70 6.20 5.78 155.90 DBD2 36.30 18.50 0.51 54.10 6.30 5.97 204.03 DBD3 36.30 18.70 0.52 53.80 5.70 5.35 257.24 DBD4 36.30 18.85 0.52 54.10 6.88 6.40 163.37 DBD5 36.30 18.95 0.52 52.00 8.02 7.42 149.33 DBD6 36.30 18.80 0.52 54.00 6.30 5.88 223.97
DBD7 36.30 18.80 0.52 54.20 8.39 7.83 232.31
Average 36.30 18.77 0.52 53.84 6.83 6.38 198.02
Norite E DBE1 36.30 18.40 0.51 58.60 8.25 7.86 156.52 DBE2 36.30 18.50 0.51 55.00 5.54 5.25 161.19 DBE3 36.30 18.55 0.51 56.40 9.55 9.03 152.58 DBE4 36.30 17.60 0.48 55.10 6.43 6.41 184.56 DBE5 36.30 18.30 0.50 57.40 7.62 7.30 155.54 DBE6 36.30 19.25 0.53 64.00 4.82 4.39 155.54 DBE7 36.30 17.95 0.49 57.20 6.25 6.11 156.52
Average 36.30 18.36 0.50 57.67 6.92 6.62 160.35
Spotted Anorthositic
Norite F
DBF1 36.30 19.40 0.53 58.70 6.60 5.97 243.36 DBF2 36.30 19.60 0.54 57.10 7.60 6.80 262.82 DBF3 36.30 19.55 0.54 57.60 9.35 8.39 168.34 DBF4 36.30 19.55 0.54 56.30 13.40 12.02 186.06 DBF5 36.30 18.45 0.51 57.80 7.26 6.90 175.82 DBF6 36.30 16.85 0.46 49.60 6.35 6.61 167.84 DBF7 36.30 16.85 0.46 49.60 7.31 7.61 182.93
Average 36.30 18.61 0.51 55.24 8.27 7.76 198.17
Anorthositic Norite G
DBG1 36.30 19.70 0.54 63.10 9.00 8.01 313.71 DBG2 36.30 19.40 0.53 61.70 7.50 6.78 262.23 DBG3 36.30 17.30 0.48 55.20 9.33 9.46 182.63 DBG4 36.30 17.65 0.49 57.00 9.07 9.01 200.68 DBG5 36.30 16.45 0.45 53.00 7.81 8.33 160.33 DBG6 36.30 16.20 0.45 52.30 7.26 7.86 154.93 DBG7 36.30 16.00 0.44 48.90 4.45 4.88 157.16 DBG8 36.30 18.50 0.51 59.30 7.23 6.85 199.13
Average 36.30 17.65 0.49 56.31 7.71 7.65 203.85
Spotted Anorthosite H
DBH1 36.30 16.90 0.47 49.50 8.15 8.46 285.81 DBH2 36.30 18.60 0.51 53.70 7.30 6.88 247.40 DBH3 36.30 18.50 0.51 53.60 8.20 7.77 197.19 DBH4 36.30 18.00 0.50 53.00 6.26 6.10 166.34 DBH5 36.30 16.80 0.46 49.30 6.70 6.99 179.97 DBH6 36.30 17.25 0.48 50.40 6.16 6.26 178.97 DBH7 36.30 17.05 0.47 49.50 7.03 7.23 283.13
Average 36.30 17.59 0.48 51.29 7.11 7.10 219.83
Mottled Anorthosite I
DBI1 36.30 16.40 0.45 47.10 7.00 7.49 256.91 DBI2 36.30 18.00 0.50 51.40 6.60 6.43 234.56 DBI3 36.30 17.20 0.47 48.90 6.18 6.30 192.33 DBI4 36.30 16.25 0.45 47.40 8.61 9.29 213.95 DBI5 36.30 18.00 0.50 51.50 6.94 6.76 201.07 DBI6 36.30 16.45 0.45 47.10 6.14 6.55 187.16 DBI7 36.30 17.10 0.47 49.10 6.29 6.45 212.13
Average 36.30 17.06 0.47 48.93 6.82 7.04 214.02
Effect of time on the tensile strength of several Bushveld Complex rock types
118
B3 Time-dependent Brazilian Indirect Tensile (BIT) Strength test results
The full set of the time-dependent test results is given in Table B3-1.
Table B3-3: Time-dependent Brazilian Indirect Tensile (BIT) strength test results
Sample ID
Sample diameter, D (mm)
Sample thickness,
T (mm)
T/D ratio Sample mass, M
(g)
Percentage of Average
tensile load, X%
Test load, kN
Time-to-failure, t (s)
SB90A1 36.30 18.90 0.52 53.40 90 7.37 27 SB90A2 36.30 19.00 0.52 53.70 90 7.37 38 SB90A3 36.30 19.10 0.53 53.90 90 7.37 1140 SB90A4 36.30 19.10 0.53 54.00 90 7.37 38 SB90A5 36.30 19.00 0.52 53.60 90 7.37 98
Average 36.30 19.02 0.52 53.72 90 7.37 268
SB85A1 36.30 18.90 0.52 53.30 85 6.98 2100 SB85A2 36.30 18.90 0.52 53.30 85 6.98 25 SB85A3 36.30 19.00 0.52 53.60 85 6.98 133 SB85A4 36.30 19.10 0.53 53.80 85 6.98 2240
SB85A5 36.30 19.00 0.52 53.70 85 6.98 364
Average 36.30 18.98 0.52 53.54 85 6.98 972
SB80A1 36.30 18.45 0.51 52.10 80 6.55 1943 SB80A2 36.30 19.00 0.52 53.40 80 6.55 6803 SB80A3 36.30 19.10 0.53 53.70 80 6.55 5680
SB80A4 36.30 18.90 0.52 53.20 80 6.55 30692 SB80A5 36.30 19.20 0.53 54.10 80 6.55 13174
Average 36.30 18.93 0.52 53.30 80 6.55 11658
SB75A1 36.30 19.05 0.52 53.80 75 6.14 126188 SB75A2 36.30 19.00 0.52 53.50 75 6.14 62122 SB75A3 36.30 18.70 0.52 53.30 75 6.14 125 SB75A4 36.30 19.10 0.53 53.90 75 6.14 199 SB75A5 36.30 18.90 0.52 53.20 75 6.14 10520
Average 36.30 18.95 0.52 53.54 75 6.14 39831
SB70A1 36.30 18.60 0.51 52.80 70 5.73 93616 SB70A2 36.30 18.95 0.52 52.20 70 5.73 258543 SB70A3 36.30 18.80 0.52 53.10 70 5.73 93481 SB70A4 36.30 19.10 0.53 53.90 70 5.73 280
Average 36.30 18.86 0.52 53.00 70 5.73 111480
SB90B1 36.30 18.20 0.50 51.70 90 6.16 1354 SB90B2 36.30 18.55 0.51 54.60 90 6.16 2130 SB90B3 36.30 18.40 0.51 52.60 90 6.16 3768 SB90B4 36.30 18.80 0.52 55.70 90 6.16 245 SB90B5 36.30 18.00 0.50 52.20 90 6.16 439
Average 36.30 18.39 0.51 53.36 90 6.16 1587
SB85B1 36.30 18.00 0.50 52.00 85 5.81 1516 SB85B2 36.30 18.20 0.50 51.90 85 5.81 2703 SB85B3 36.30 18.20 0.50 51.70 85 5.81 2858 SB85B4 36.30 18.55 0.51 54.60 85 5.81 1502
SB85B5 36.30 18.40 0.51 52.60 85 5.81 2422
Average 36.30 18.27 0.50 52.56 85 5.81 2200
SB80B1 36.30 18.80 0.52 55.70 80 5.47 16964 SB80B2 36.30 18.00 0.50 52.20 80 5.47 149 SB80B3 36.30 18.00 0.50 52.00 80 5.47 4805 SB80B4 36.30 18.20 0.50 51.90 80 5.47 140 SB80B5 36.30 18.70 0.52 55.30 80 5.47 832
Average 36.30 18.34 0.51 53.42 80 5.47 4578
SB75B1 36.30 18.40 0.51 52.60 75 5.13 73429 SB75B2 36.30 18.70 0.52 55.30 75 5.13 641 SB75B3 36.30 18.00 0.50 51.50 75 5.13 1886 SB75B4 36.30 18.40 0.51 52.55 75 5.13 5994 SB75B5 36.30 18.40 0.51 52.57 75 5.13 17234
Average 36.30 18.38 0.51 52.90 75 5.13 19837
SB70B1 36.30 18.20 0.50 51.90 70 4.79 58681 SB70B2 36.30 18.15 0.50 50.40 70 4.79 85504 SB70B3 36.30 18.18 0.50 50.40 70 4.79 19691 SB70B4 36.30 18.15 0.50 50.40 70 4.79 85027
Average 36.30 18.17 0.50 50.78 70 4.79 62226
SB90C1 36.30 18.20 0.50 60.20 90 6.69 1080
Effect of time on the tensile strength of several Bushveld Complex rock types
119
SB90C2 36.30 19.20 0.53 63.10 90 6.69 32580
SB85C1 36.30 19.20 0.53 62.00 85 6.32 71041 SB85C2 36.30 18.75 0.52 61.30 85 6.32 6349
Average 36.30 18.98 0.52 61.65 85 6.32 38695
SB80C1 36.30 18.90 0.52 62.20 80 5.94 33705
Average 36.30 18.90 0.52 62.20 80 5.94 33705
SB75C1 36.30 18.75 0.52 61.50 75 5.57 207423
Average 36.30 18.75 0.52 61.50 75 5.57 207423
SB70C1 36.30 19.05 0.52 62.60 70 5.20 3840 SB70C2 36.30 19.30 0.53 63.40 70 5.20 88441 SB70C4 36.30 19.05 0.52 62.60 70 5.20 2013 SB70C5 36.30 19.30 0.53 63.40 70 5.20 126
Average 36.30 19.18 0.53 63.00 70 5.20 23605
SB90D1 36.30 18.85 0.52 54.10 90 6.15 220 SB90D2 36.30 18.50 0.51 54.10 90 6.15 340 SB90D3 36.30 18.95 0.52 52.00 90 6.15 259 SB90D5 36.30 18.80 0.52 54.20 90 6.15 96
Average 36.30 18.78 0.52 53.60 90 6.15 229
SB85D1 36.30 18.77 0.52 54.10 85 5.81 1495 SB85D2 36.30 18.5 0.51 52.00 85 5.81 72424 SB85D3 36.30 18.95 0.52 54.00 85 5.81 1056 SB85D4 36.30 18.8 0.52 54.20 85 5.81 5358 SB85D5 36.30 18.8 0.52 54.20 85 5.81 146 SB85D6 36.30 18.8 0.52 55.20 85 5.81 17487
Average 36.30 18.77 0.52 53.95 85 5.81 16328
SB80D1 36.30 18.85 0.52 54.10 80 5.46 14525 SB80D2 36.30 18.5 0.51 54.10 80 5.46 6070 SB80D3 36.30 18.95 0.52 52.00 80 5.46 36173
SB80D4 36.30 18.8 0.52 54.00 80 5.46 85861 SB80D5 36.30 18.8 0.52 54.20 80 5.46 270873
Average 36.30 18.78 0.52 53.68 80 5.46 82700
SB75D1 36.30 18.85 0.52 54.10 75 5.12 6023 SB75D2 36.30 18.5 0.51 54.10 75 5.12 75876 SB75D3 36.30 18.95 0.52 52.00 75 5.12 20808 SB75D4 36.30 18.8 0.52 54.00 75 5.12 20878 SB75D5 36.30 18.8 0.52 54.20 75 5.12 76824 SB75D6 36.30 18.8 0.52 54.20 75 5.12 17429
Average 36.30 0.52 53.77 75 5.12 36306
SB70D1 36.30 18.85 0.52 54.10 70 4.78 232577 SB70D2 36.30 18.5 0.51 54.10 70 4.78 71201
Average 36.30 18.68 0.51 54.10 70 4.78 151889
SB90E1 36.30 18.40 0.51 58.60 90 6.23 2901 SB90E2 36.30 17.60 0.48 55.10 90 6.23 402
Average 36.30 18.00 0.50 56.85 90 6.23 1652
SB85E1 36.30 18.4 0.51 58.60 85 5.88 556 SB85E2 36.30 17.6 0.48 55.10 85 5.88 193
Average 36.30 18.00 0.50 56.85 85 5.88 375
SB80E1 36.30 18.4 0.51 58.60 80 5.54 1563 SB80E2 36.30 17.6 0.48 55.10 80 5.54 3529 SB80E3 36.30 18.3 0.50 57.40 80 5.54 25890
Average 36.30 18.10 0.50 57.03 80 5.54 10327
SB75E1 36.30 18.4 0.51 58.60 75 5.19 203 SB75E2 36.30 17.6 0.48 55.10 75 5.19 100 SB75E3 36.30 18.3 0.50 57.40 75 5.19 2933 SB75E4 36.30 19.25 0.53 64.00 75 5.19 5138 SB75E5 36.30 17.95 0.49 57.20 75 5.19 22
Average 36.30 18.30 0.50 58.46 75 5.19 1679
SB70E1 36.30 18.4 0.51 58.60 70 4.84 179689 SB70E2 36.30 17.6 0.48 55.10 70 4.84 2287 SB70E3 36.30 18.3 0.50 57.40 70 4.84 142 Average 36.30 18.10 0.50 57.03 70 4.84 60706 SB85F1 36.30 19.55 0.54 57.60 85 7.03 556 SB85F2 36.30 19.55 0.54 56.30 85 7.03 193
Average 36.30 19.55 0.54 56.95 85 7.03 375
SB80F1 36.30 19.55 0.54 57.60 80 6.62 1564 SB80F2 36.30 19.55 0.54 56.30 80 6.62 3529 SB80F3 36.30 18.45 0.51 57.80 80 6.62 21 Average 36.30 19.18 0.53 57.23 80 6.62 1705 SB75F1 36.30 19.55 0.54 57.60 75 6.20 2933 SB75F2 36.30 19.55 0.54 56.30 75 6.20 5138 SB75F3 36.30 18.45 0.51 57.80 75 6.20 22
Average 36.30 19.18 0.53 57.23 75 6.20 2698
SB70F1 36.30 19.55 0.54 57.60 70 5.79 179699
Effect of time on the tensile strength of several Bushveld Complex rock types
120
SB70F2 36.30 19.55 0.54 56.30 70 5.79 2287 SB70F3 36.30 18.45 0.51 57.80 70 5.79 142
Average 36.30 19.18 0.53 57.23 70 5.79 60709
SB90G1 36.30 17.3 0.48 55.20 90 6.94 643
Average 36.30 17.30 0.48 55.20 90 6.94 643
SB85G2 36.30 17.65 0.49 57.00 85 6.55 147
Average 36.30 17.65 0.49 57.00 85 6.55 147
SB75G5 36.30 18.00 0.50 53.00 75 5.78 2483 SB75G6 36.30 18.00 0.50 53.00 75 5.78 2483
Average 36.30 18.00 0.50 53.00 75 5.78 2483
SB70G1 36.30 17.25 0.48 53.20 90 5.40 795 SB70G2 36.30 17.05 0.47 55.20 90 5.40 1306 SB70G3 36.30 16.90 0.47 54.70 90 5.40 313
Average 36.30 17.07 0.47 54.37 90 5.40 805
SB90H1 36.30 18 0.50 53.00 90 6.40 7308 SB90H2 36.30 16.8 0.46 49.30 90 6.40 6256 SB90H3 36.30 17.25 0.48 50.40 90 6.40 5477 SB90H4 36.30 17.05 0.47 49.50 90 6.40 1232 SB90H5 36.30 16.9 0.47 49.50 90 6.40 796
Average 36.30 17.20 0.47 50.34 90 6.40 4214
SB85H1 36.30 18 0.50 53.00 85 6.04 28432 SB85H2 36.30 16.8 0.46 49.30 85 6.04 6949 SB85H3 36.30 17.25 0.48 50.40 85 6.04 1889 SB85H4 36.30 17.05 0.47 49.50 85 6.04 11895
Average 36.30 17.28 0.48 50.55 85 6.04 12291
SB80H1 36.30 18.85 0.52 54.10 80 5.69 94 SB80H2 36.30 18.5 0.51 54.10 80 5.69 29908 SB80H3 36.30 18.95 0.52 52.00 80 5.69 451 SB80H4 36.30 18.8 0.52 54.00 80 5.69 10996 SB80H5 36.30 18.8 0.52 54.20 80 5.69 1898 SB80H6 36.30 18.8 0.52 54.20 80 5.69 5662
Average 36.30 18.78 0.52 53.77 80 5.69 8168
SB75H1 36.30 18 0.50 53.00 75 5.33 7926 SB75H2 36.30 16.8 0.46 49.30 75 5.33 76443 SB75H3 36.30 17.25 0.48 50.40 75 5.33 1561 SB75H4 36.30 17.05 0.47 49.50 75 5.33 7942 SB75H5 36.30 16.9 0.47 49.50 75 5.33 241671
Average 36.30 17.20 0.47 50.34 75 5.33 67109
SB70H1 36.30 17.20 0.47 48.90 70 4.98 10092 SB70H2 36.30 16.25 0.45 47.40 70 4.98 4695 SB70H3 36.30 16.40 0.45 47.10 70 4.98 147976 SB70H4 36.30 16.45 0.45 47.10 70 4.98 9014 SB70H5 36.30 17.10 0.47 49.10 70 4.98 62350 SB70H6 36.30 17.10 0.47 49.10 70 4.98 13179
Average 36.30 16.68 0.46 47.92 70 4.98 46825
SB90I1 36.30 17.20 0.47 48.90 90 6.14 229 SB90I2 36.30 17.10 0.47 49.10 90 6.14 1370 SB90I3 36.30 16.45 0.45 47.10 90 6.14 417 SB90I4 36.30 16.50 0.45 47.90 90 6.14 27865 SB90I5 36.30 16.50 0.45 47.90 90 6.14 1183
Average 36.30 16.75 0.46 48.18 90 6.14 6213
SB85I1 36.30 17.20 0.47 48.90 85 5.80 56 SB85I2 36.30 17.10 0.47 49.10 85 5.80 67322 SB85I3 36.30 16.45 0.45 47.10 85 5.80 206 SB85I4 36.30 16.50 0.45 47.90 85 5.80 158217 SB85I5 36.30 16.50 0.45 47.900 85 5.80 154
Average 36.30 16.75 0.46 48.18 85 5.80 45191
SB80I1 36.30 17.20 0.47 48.90 80 5.46 26295 SB80I2 36.30 17.10 0.47 49.10 80 5.46 104174 SB80I3 36.30 16.45 0.45 47.10 80 5.46 1653 SB80I4 36.30 16.50 0.45 47.90 80 5.46 28
Average 36.30 16.81 0.46 48.25 80 5.46 33038
SB75I1 36.30 17.20 0.47 48.90 75 5.12 58565 SB75I2 36.30 17.10 0.47 49.10 75 5.12 11801 SB75I3 36.30 16.45 0.45 47.10 75 5.12 94169 SB75I4 36.30 16.50 0.45 47.90 75 5.12 8910 SB75I5 36.30 16.50 0.45 47.9 75 5.12 21521
Average 36.30 16.75 0.46 48.18 75 5.12 38993
SB70I1 36.30 17.20 0.47 48.90 70 4.77 40685 SB70I2 36.30 17.10 0.47 49.10 70 4.77 13602 SB70I3 36.30 16.45 0.45 47.10 70 4.77 139456 SB70I4 36.30 16.50 0.45 47.90 70 4.77 431 SB70I5 36.30 16.50 0.45 47.90 70 4.77 1583
Average 36.30 16.75 0.46 48.18 70 4.77 39151
Effect of time on the tensile strength of several Bushveld Complex rock types
121
Percentage tensile strength-time plots of the nine test categories are presented here.
The results show huge variation that a logarithmic trend line is plotted here. The
general trend shows a time-dependency with the short times to failure for test loads
between 80 and 90% of the tensile strength and prolonged failure times for the tests
loads below 80% of the tensile strength.
Figure B3-1: Time-to-failure plots: (mottled anorthosite)
% Tensile Strength = -1.663ln(Time) + 92.507 R² = 0.5053
0
10
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70
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90
100
0 50000 100000 150000 200000 250000 300000
% o
f te
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le s
tre
ngt
h
Time-to-failure (s)
% tensile strength-Time (A)
Average Time-to-failure
Test set 1
Test set 2
Test set 3
Test set 4
Test set 5
Logarithmic trend line
Effect of time on the tensile strength of several Bushveld Complex rock types
122
Figure B3-2: Time-to-failure plots: (spotted anorthositic norite)
Figure B3-3: Time-to-failure plots: (pyroxenite)
%Tensile Strength = -5.018ln(Time) + 124.59 R² = 0.8008
0
10
20
30
40
50
60
70
80
90
100
0 20000 40000 60000 80000 100000
% o
f te
nsi
le s
tre
ngt
h
Time-to-failure (s)
% tensile strength-Time (B)
Average time-to-failure
Test set 1
Test set 2
Test set 3
Test set 4
Test set 5
Test set 6
Logarithmic trend line
% Tensile Strength = -8.454ln(Time) + 174.23 R² = 0.5641
0
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20
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40
50
60
70
80
90
100
0 50000 100000 150000 200000 250000
% o
f te
nsi
le s
tre
ngh
Time to-failure (s)
% tensile strength-Time (C)
Average time-to-failure
Test set 1
Test set 2
Test set
Test set 4
Logarithmic trend line
Effect of time on the tensile strength of several Bushveld Complex rock types
123
Figure B3-4: Time-to-failure plots: (mottled anorthosite)
Figure B3-5: Time-to-failure plots: (norite)
% Tensile Strength = -2.834ln(Time) + 104.57 R² = 0.8689
0
10
20
30
40
50
60
70
80
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100
0 50000 100000 150000 200000 250000 300000
% o
f te
nsi
le s
tre
ngt
h
Time-to-failure (s)
% tensile strength-time (D)
Average time-to-failure
Test set 1
Test set 2
Test set 3
Test ser 4
Test set 5
Test set 6
Logarithmic trend line
% Tensile Strength = -1.947ln(Time) + 93.166 R² = 0.9235
0
10
20
30
40
50
60
70
80
90
100
0 50000 100000 150000 200000
% o
f te
nsi
le s
tre
ngt
h
Time-to-failure (s)
% tensile strength-Time (E)
Average time-to-failure
Test set 1
Test set 2
Test set 3
Test set 4
Test set 5
Logarithmic trend line
Effect of time on the tensile strength of several Bushveld Complex rock types
124
Figure B3-6: Time-to-failure plots: (spotted anorthositic norite)
Figure B3-7: Time-to-failure plots: (anorthositic norite)
% Tensile Strength = -1.422ln(Time) + 88.18 R² = 0.4642
0
10
20
30
40
50
60
70
80
90
0 50000 100000 150000 200000
% o
f te
nsi
le s
tre
ngt
h
Time-to-failure (s)
% tensile strength-Time (F)
Average time-to-failure
Test set 1
Test set 2
Test set 3
Test set 5
Logarithmic trend line
% Tensile Strength = -1.823ln(Time) + 93.024 R² = 0.2154
0
10
20
30
40
50
60
70
80
90
100
0 10000 20000 30000 40000
% o
f te
nsi
le s
tre
ngt
h
Time-to-failure (s)
% tensile strength-Time (G)
Average time-to-failure
Test set 1
Test set 2
Test set 3
Test set 4
Logarithmic trend line
Effect of time on the tensile strength of several Bushveld Complex rock types
125
Figure B3-8: Time-to-failure plots: (spotted anorthosite)
Figure B3-9: Time-to-failure plots: (mottled anorthosite)
% Tensile Strength = -2.752ln(Time) + 105.73 R² = 0.6295
0
10
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30
40
50
60
70
80
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100
0 50000 100000 150000 200000 250000 300000
% o
f te
nsi
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tre
ngt
h
Time-to-failure (s)
% tensile strength-Time (H) Average time-to-failure
Test set 1
Test set 2
Test set 3
Test set 4
Test set 5
Test set 6
Test set 7
Test set 8
Test set 9
Test set 10
Logarithmic trend line
% Tensile Strength = -2.113ln(Time) + 100.23 R² = 0.5057
0
10
20
30
40
50
60
70
80
90
100
0 50000 100000 150000 200000
% tensile strength-Time (I)
Average time-to-failure
Test set 1
Test set 2
Test set 3
Test set 4
Test set 5
Test set 6
Test set 7
Logarithmic trend line
Effect of time on the tensile strength of several Bushveld Complex rock types
126
Appendix C: Numerical modelling results (Stress and strain analysis)
C1 Stress and strain analysis: Incline shaft
Models of an incline shaft and a stope were analysed in a similar way to the in-stope
pillar models. These models were run to validate the observations made in the in-
stope pillar models presented in Chapter 3 with differently shaped models. Major
Principal Stress contours for four different scenarios are shown in Figures C1-1 to 1-
4.
Major principal stress contours: Depth = 500m and k-ratio = 1
Figure C1-1: Major Principal Stress at a depth of 500m with k-ratio = 1
Effect of time on the tensile strength of several Bushveld Complex rock types
127
Major principal stress contours: Depth = 500m and k-ratio = 2
Figure C1-2: Major Principal Stress at a depth of 500m with k-ratio = 2
Major principal stress contours: Depth = 1000m and k-ratio = 1
Figure C1-3: Major Principal Stress at a depth of 1000m with k-ratio = 1
Effect of time on the tensile strength of several Bushveld Complex rock types
128
Major principal stress contours: Depth = 1000m and k-ratio = 2
Figure C1-4: Major Principal Stress at a depth of 1000m with k-ratio = 2
Minor principal stress contours: Depth = 500m and k-ratio = 1
Figure C1-5: Minor Principal Stress at a depth of 500m with k-ratio = 1
Effect of time on the tensile strength of several Bushveld Complex rock types
129
Figure C1-6: Minor Principal Stress at a depth of 500m with k-ratio = 2. The depth of influence of low compressive and tensile stresses is indicated
Minor principal stress contours: Depth = 1000m and k-ratio = 1
Figure C1-7: Minor Principal Stress at a depth of 1000m with k-ratio = 1
Effect of time on the tensile strength of several Bushveld Complex rock types
130
Minor principal stress contours: Depth = 1000m and k-ratio = 2
Figure C1-8: Minor Principal Stress at a depth of 1000m with k-ratio = 2
Extension strain contours: Depth = 500m and k-ratio = 1
Figure C1-9: Extension strain at a depth of 500m with k-ratio = 1
Effect of time on the tensile strength of several Bushveld Complex rock types
131
Extension strain contours: Depth = 500m and k-ratio = 2
Figure C1-10: Extension strain at a depth of 500m with k-ratio = 2
Extension strain contours: Depth = 1000m and k-ratio = 1
Figure C1-11: Extension strain at a depth of 1000m with k-ratio = 1
Effect of time on the tensile strength of several Bushveld Complex rock types
132
Extension strain contours: Depth = 1000m and k-ratio = 2
Figure C1-12: Extension strain at a depth of 1000m with k-ratio = 2
Figures C1-5 to C1-8 show the excavation walls under stress conditions ranging
from tensile (-2 MPa) to very low compressive stress (maximum 5.7 MPa) at a depth
of 500m and k = 1. Similar low compressive stress trends were shown for the other
loading conditions with the deepest low compression influence being 3.589 m into
the hanging wall. The extension strain contours are shown in Figures C1-9 to C1-12.
The immediate walls of the excavation were observed to experience negative
extension strain implying the probability of fracture initiation in these walls. Very low
confinement is experienced in the walls of the excavation, conditions conducive for
spalling of the wall rock. In the BC mine excavations confinement is often provided
by installed area cover support, curbing the spalling in life of mine excavations.
Analysis of stress-strain in a mining stope follows in appendix C2.
C2 Stress and strain analysis: mining stope
Results of stress-strain analysis of a mining stope are presented in Figures C2-1 to
C2-4.
Effect of time on the tensile strength of several Bushveld Complex rock types
133
Major principal stress contours: Depth = 500m and k-ratio = 1
Figure C2-1: Major Principal Stress at a depth of 500m with k-ratio = 1
Major principal stress contours: Depth = 500m and k-ratio = 2
Figure C2-2: Major Principal Stress at a depth of 500m with k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
134
Major principal stress contours: Depth = 1000m and k-ratio = 1
Figure C2-3: Major Principal Stress at a depth of 1000m with k-ratio = 1
Major principal stress contours: Depth = 1000m and k-ratio = 2
Figure C2-4: Major Principal Stress at a depth of 1000m with k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
135
Notice the similarity in the pictures of contour plots with the in-stope pillar models
already presented in chapter 3. It is observed here that the excavation walls are
under very low compressive stress, similar to the observations made in the in-stope
pillar and incline shaft models. Minor principal stress contours are shown in Figures
C2-5 to C2-8.
Minor principal stress contours: Depth = 500m and k-ratio = 1
Figure C2-5: Minor Principal Stress at a depth of 500m with k-ratio = 1
Figure C2-6: Minor Principal Stress at a depth of 500m with k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
136
Minor principal stress contours: Depth = 1000m and k-ratio = 1
Figure C2-7: Minor Principal Stress at a depth of 1000m with k-ratio = 1
Minor principal stress contours: Depth = 1000m and k-ratio = 2
Figure C2-8: Minor Principal Stress at a depth of 1000m with k-ratio = 2
Notice how the periphery of the stope is largely under very low compressive stress
and in some instances tensile stress.
Effect of time on the tensile strength of several Bushveld Complex rock types
137
Extension strain contours: Depth = 500m and k-ratio = 1
Figure C2-9: Extension strain at a depth of 500m with k-ratio = 1
Figure C2-10: Extension strain at a depth of 500m with k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
138
Extension strain contours: Depth = 1000m and k-ratio = 1
Figure C2-11: Extension strain at a depth of 1000m with k-ratio = 1
Extension strain contours: Depth = 1000m and k-ratio = 2
Figure C2-12: Extension strain at a depth of 1000m with k-ratio = 2
Effect of time on the tensile strength of several Bushveld Complex rock types
139
Notice how the extension strain contours take a sub-horizontal direction in the
hanging wall in line with the expected principal stresses existing in the shallow
Bushveld Complex mines.